October 2009
Monogamy of Bell’s Inequality Violations in Nonsignaling Theories
Physical Review Letters 102, 030403 (2009)
M. Pawlowski and C. Brukner
Overview
The nonsignaling principle—the impossibility of sending information faster
than the speed of light—is deeply rooted in our existing understanding of the
physical world. It not only allows us to consider current physical theories
within a general framework of the nonsignaling principle, but also to
significantly restrict the structure of possible future ("postquantum")
theories.
Quantum theory predicts correlations between spacelike separated events, which
are nonsignaling but cannot be explained within local realism, i.e., within the
framework in which all outcomes have pre-existing values for any possible
measurement before the measurements are made (‘‘realism’’) and where these
values are independent from any action at spacelike separated regions
(‘‘locality’’) [1]. This is signified by the violation of Bell’s inequalities.
Since the work of Popescu and Rohrlich [2], it is known that there are
correlations violating Bell’s inequality stronger than the quantum mechanical
correlations, but without contradicting the nonsignaling principle.
The general framework for considering nonsignaling correlations is also
important from the information-theoretical point of view. For example, protocols
for a secret key distribution were recently proposed and their security proved
solely using the nonsignaling principle [3-4]. The important properties of a
theory that allows extraction of secret key are "monogamy" relations for
correlations: an increase of strength in correlations (as measured by violation
of Bell's inequalities) between trusted persons Alice and Bob is always at the
expense of a corresponding decrease of the strength in correlations between
Alice and the spy Eve (or Bob and Eve).
In Physical Review Letter [5] two QAP researchers -- Pawlowski and Brukner --
derived monogamy relations (tradeoffs) between strengths of violations of Bell’s
inequalities in any non-signaling theory. Their result applies to general Bell
inequalities with an arbitrary large number of partners, outcomes, and
measurement settings. The method is simple, efficient, and does not require
linear programming. The results are used to derive optimal fidelity for
asymmetric cloning in nonsignaling theories.
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Diagram of measurements involved in the monogamy relation for violation of Bell inequalities between Alice and Bob 1, Alice and Bob 2 etc. |
References
[1] J. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).
[2] S. Popescu and D. Rohrlich, Found. Phys. 24, 379 (1994).
[3] J. Barrett, L. Hardy, and A. Kent, Phys. Rev. A 71, 022101 (2005).
[4] A. Acin, N. Gisin, and Ll. Masanes, Phys. Rev. Lett. 97, 120405 (2006).
[5] M. Pawlowski and C. Brukner, Phys. Rev. Lett. 102, 030403 (2009).
September 2009
Most
quantum states are too entangled to be useful as computational resources
[1] D. Gross, S.T. Flammia, J. Eisert, Physical Review Letters
102, 190501 (2009).
[2] M.J. Bremner, C. Mora, A. Winter, Physical Review Letters 102, 190502 (2009).
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A classical computer endowed with the power to perform measurements on certain entangled many-body states is strongly believed to be exponentially more powerful than a classical machine alone. Indeed, a computer having access to local measurements on a cluster state [3] or the class of states identified in Refs. [4-7] can efficiently simulate any quantum computation. The best-known classical algorithm for this task requires super-polynomial run time and it is strongly believed that no substantial improvement is possible. It is in this sense that certain many-body states possess strong computational power. More precisely, the particular states mentioned above are computationally universal in that they enable a classical machine to efficiently solve any problem in the complexity class BQP.
One is thus led to the questions: How common is the property of offering universal computational speed-ups and what is the role of entanglement in this context?
All previous results which rule out computational universality of certain quantum systems seem to do so by either (i) showing that the systems are not entangled enough to support a universal quantum calculation [8-11] or (ii) relying on stringent symmetries [12,13]. It is therefore reasonable to conjecture, by extrapolating from the current lines of research, that in generic situations "more entanglement" will imply "more computational power".
Going further, it has been realized (using sundry techniques known under the label of the "probabilistic method" or the "concentration of measure phenomenon") that generic quantum states are extremely highly entangled from many points of view [14]. For example, a typical state is almost maximally entangled with respect to any partition of its systems into two parties. It follows that most states are excellent resources for some quantum information protocols, e.g. teleportation with respect to any bipartition. Thus, it is plausible to suspect that offering a computational speed-up is a generic feature of quantum states, if only advanced enough classical control schemes could be devised to utilize their power.
QAP researchers [1] (see also [2]) have found, however, that quite counter-intuitively, quantum states can be "too entangled" to serve as computational resources for measurement-based quantum computation.
Once the entanglement contained in a state (quantified in terms of the geometric measure) reaches a certain threshold, no computational speedup can be facilitated by performing local measurements on that state. The result is not limited to a specific protocol, but covers any scheme based on local measurements and efficient classical post-processing.
In a sense, the phenomenon arises because the output distribution of any local measurement protocol is too close to that of a fair coin to be of use. Bear in mind that the occurrence of some form of randomness is inherent to any non-trivial quantum measurement. Protocols which do achieve a computational speedup on less entangled quantum states go through some length to compensate for that unavoidable randomness - essentially by reading the results of the computation off the correlations instead of the individual measurement outcomes as such. The novel result can be phrased as saying that, for highly entangled states, no such trick exists.
What is more, it is shown that the geometric entanglement contained in a generic state is high enough for this effect to occur. The authors sketch some schemes for the direct, efficient construction of states containing a very high amount of geometric entanglement and showing signatures of the phenomenon.
So, states can not only be too little entangled for quantum computation, but also too entangled, raising yet again the question of the precise origin of the computational speedup of a quantum computer. After all, it shows that as with most good things, entanglement is best used in moderation.
References
[3] R. Raussendorf and H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001); R. Raussendorf and H.J. Briegel, Quant. Inf. Comp. 6, 433 (2002).
[4] D. Gross and J. Eisert, Phys. Rev. Lett. 98, 220503 (2007).
[5] D. Gross, J. Eisert, N. Schuch, and D. Perez-Garcia, Phys. Rev. A 76, 052315 (2008); D. Gross and J. Eisert, arxiv:0810.2542.
[6] M. Van den Nest, W. Duer, A. Miyake, and H. J. Briegel, New J. Phys. 9, 204 (2007).
[7] G.K. Brennen and A. Miyake, Phys. Rev. Lett. 101, 010502 (2008).
[8] M. Van den Nest, A. Miyake, W. Duer, and H.J. Briegel, Phys. Rev. Lett. 97, 150504 (2006).
[9] M. Van den Nest, W. Duer, G. Vidal, and H.J. Briegel, Phys. Rev. A 75, 012337 (2007).
[10] G. Vidal, Phys. Rev. Lett. 98, 070201 (2007).
[11] I.L. Markov and Y. Shi, SIAM J. Comp. 38, 963 (2008).
[12] D. Gottesman, PhD thesis (CalTech, Pasadena, 1997).
[13] R. Jozsa and A. Miyake, Proc. R. Soc. A 464, 3089 (2008).
[14] P. Hayden, D. Leung, P.W. Shor, and A. Winter, Commun. Math. Phys. 250,371 (2004); P. Hayden, D.W. Leung, and A. Winter, Comm. Math. Phys. 265, 95 (2006).
May 2009
Optimal fidelity of
teleportation of coherent states and entanglement
Physical Review Letters A 78, 062340 (2008) [9 pages]
http://link.aps.org/doi/10.1103/PhysRevA.78.062340
A. Mari and D. Vitali
Quantum teleportation is the transfer of an unknown quantum state from a sender to a receiver , which can be realized if the two parties share a specific quantum property, entanglement, and can exchange information through a standard communication channel. It has been proposed in 1993 [1] and then experimentally demonstrated in a variety of physical systems, involving either qubits [2] and continuous variable (CV) systems [3], i.e., characterized by a continuous degree of freedom, such as a particle with its position, or an optical mode with its electric field.
The success of teleportation is quantified by the fidelity, which is the probability of finding the input state at the receiver station, and it can reach the maximum value of 1 only if the entanglement shared by the two parties is maximum (and, obviously, the information through the classical channel is appropriately exploited).
The relation between the shared entanglement and the achievable fidelity is non-trivial, especially in the CV case. In fact, differently from entanglement, teleportation fidelity is not invariant under local operations at the two stations, i.e., it can be increased or decreased by adjusting the local settings, even at a fixed shared entanglement.
This fact raises two questions: i) which
is the maximum achievable fidelity for a given entanglement; ii) which is the
optimal local operation maximizing the fidelity. These questions have been
partially answered in [4,5], but in the present paper they have been completely
solved for the optimization of teleportation of coherent states via local
Gaussian operations. In fact, it is shown that for a given entanglement,
quantified by the logarithmic negativity EN, [6], the optimal
fidelity F satisfies the two bounds
The two bounds are quite tight and therefore provide a good estimate of the achievable fidelity, as shown by the plot below
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| Figure 1: Upper and lower bounds, for the fidelity of teleportation of coherent states versus n = exp[EN]. The blue shaded region is the allowed region in the (F,n) plane. |
The paper has also determined which is the optimal local Gaussian operation. It can always decomposed in terms of single operations which are easy to implement on optical modes (using phase shifters, beam splitters and squeezers) and for this reason the result is particularly useful for optical implementations. It can be extended however also to optomechanical settings, in which one can teleport the state of an optical field onto a mechanical resonator [7], because the operations can be confined only to the “optical” part of the shared entangled state.
References
[1] C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[2] D. Bouwmeester et al., Nature (London) 390, 575 (1997) ;D. Boschi et al., Phys. Rev. Lett. 80, 1121 (1998).
[3] A. Furusawa et al., Science 282, 706 (1998); N. Takei, H. Yonezawa, T. Aoki, and A. Furusawa,
Phys. Rev. Lett. 94, 220502 (2005); J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. S. Polzik, Nature (London) 443, 557 (2006).
[4] J. Fiurasek, Phys. Rev. A 66, 012304 (2002).
[5] G. Adesso and F. Illuminati, Phys. Rev. Lett. 95, 150503 (2005).
[6] J. Eisert, Ph.D. thesis, University of Potsdam, 2001; G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. A. 70, 022318 (2004).
[7] S. Mancini, D. Vitali, P. Tombesi, Phys. Rev. Lett. 90, 137901 (2003).
April 2009
Ultralong spin coherence time in isotopically engineered diamond
Nature Materials 8, 383 - 387 (2009)
G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi1, J. Isoya, J. Achard, J. Beck, J. Tisler, V. Jacques, P. R. Hemmer, F. Jelezko and J. Wrachtrup
Overview
Apart from being valuable gem stones, diamonds possess superior material
properties, which are of immense use in modern technology. Diamond tops in
certain properties like thermal conductivity, hardness, charge carrier mobility,
chemical inertness and optical transparency. In addition to these properties,
doped diamond is gaining importance in the thriving age of spintronics.
Diamond crystals on doping with Nitrogen atoms forms defect centers called
Nitrogen – Vacancy (NV) color centers. The structure of NV center consists of
substitutional nitrogen at the lattice site neighboring a carbon vacancy (Figure
1a). Several unique properties make the NV centers particularly suitable for
applications related to quantum information processing. Firstly the NV center
exhibit strong optical absorption and high fluorescence yield that allows us to
detect and address single defect centers using confocal fluorescence microscopy.
Secondly it is an extraordinarily photostable single photon source. Third being
the paramagnetic ground state of a NV defect can be used as qubit. Finally the
fluorescence intensity of a NV defect is spin dependent, which allow us to
readout the spin state via counting the number of scattered photons.
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Figure 1: (a) Structure of a Nitrogen-Vacancy center in diamond. (b) Energy level scheme of the NV defect center. (c) Ultra long spin coherence time (T2~1.8ms) in isotopically engineered diamond. (d) Nanoscale magnetic field sensing using a single NV center Quantum grade diamond. |
The negative charge state of the defect center is formed by three electrons
associated with dangling bonds of vacancy, and the two electrons of the nitrogen
and additional electron form an external donor. Two out of six electrons are
unpaired forming a triplet spin system. Spin-spin interactions spit the energy
levels with magnetic quantum numbers ms=0 and ms=1 by
about 2.88 GHz. The degeneracy of ms +/- 1 state that arise because
of the C3v symmetry can be lifted further by applying external
magnetic field (Figure 1b). Under optical illumination, spin-selective
relaxations lead to an efficient optical pumping of the system into ms=0
state that allows fast initialization of the spin qubit. The spin state of a NV
defect can be manipulated by applying resonant microwave fields. Hence all the
necessary ingredients to prepare, manipulate and readout single spin qubit are
readily available in diamond. Single defects can be isolated and individually
addressed using confocal microscopy and nonlinear microscopic techniques that
allow far field addressing of defects with a few nanometers spatial resolution.
NV centers in diamonds are robust spin system because of its coherence time is
weakly affected by temperature. The two principal causes of decoherence in NV
center in diamond are due to the magnetic field fluctuations caused by spins of
substitutional nitrogen impurity and the presence of 13C isotope in
the diamond lattice. Advances in synthetic diamond growth has successfully
minimized these two factors, thus promoting diamond based spin systems to have
ultra long coherence times ever achieved for a solid state system at room
temperature. In this paper, the coherence time of about 1.8 ms is achieved for a
NV spin in diamond made up of 99.7% of 12C isotopes and Nitrogen
content less than 1 ppb. (Figure 1c) Such a Quantum grade diamond offers a spin
free lattice and preserves the spin coherence time of the qubit very long,
enabling numerous benchmark experiments in quantum information processing.
Taking into account the time required for single qubit gate of a few nanoseconds
and a MHz speed for two-qubit CNOT, fidelity limit necessary for quantum error
correction come within reach. Furthermore, ultra long coherence times
potentially allow building quantum register based on magnetic dipolar coupling
between isolated NV spins. The strength of dipolar interaction is in the range
of few kHz for qubits spaced few tens of nanometers apart. Hence quantum
register with individual addressable qubits using nonlinear microscopy technique
can potentially be build at room temperature in solid state.
One application that was demonstrated is for sensing very weak magnetic fields.
Using a single NV defect center magnetic fields as small as few nanoTesla was
measured, with a sensitivity of about 4nT/√Hz (Figure 1d). Such sensitivity
would allow probing external spins by measuring the coupling/decoherence.
Nanoscale positioning/scanning offers advantages in developing novel microscope
capable of imaging magnetic fields of nanostructure. Being an atomistic sensor,
scanning them over the samples/molecules of interest would readily give the
image of spin densities and dynamics. The method has far reaching potential in
solving structure of biomolecules under ambient conditions. These NV
magnetometers also find applications in sensing weak magnetic fields associated
with ion currents through membrane channels in living cells.
February 2009
Identical
photons from a semiconductor diode
Applied Physics Letters 92, 193503 (2008)
A.J. Bennett, R. B. Patel, A.J. Shields, K. Cooper, P. Atkinson, C.A.
Nicoll, and D. A. Ritchie
Real-world applications of optical quantum information processing could become
more practical if small and robust light sources were available that could
generate identical, single photons. An experimental test of whether two photons
are identical can be made by colliding two photons at a 50% reflecting, 50%
transmitting mirror: if they are identical a quantum interference effect occurs
whereby both photons exit along the same direction, as illustrated in Figure 1.
This effect is the cornerstone of many proposed quantum computing schemes which
operate with light.
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| Figure 1: If two photons are incident on the 50% reflecting, 50% transmitting mirror we might expect that there are four possibilities for how those photons can exit, which are shown in (a)-(d). However, quantum mechanics tells if the photons are identical events (a) and (b) cancel out, so we will only observed the photons leaving together, as shown in (e). |
Our goal was to demonstrate that it is possible to observe this effect with a
simple light emitting diode (LED). Most LEDs currently produced emit
uncontrolled numbers of photons at random times and with variable energies. Thus
any given photon is unlikely to be identical to the others. For the last few
years we have been developing a particular type of LED that contains a single
semiconductor quantum dot, which is capable of emitting single photons, one at a
time. Our recent advance is to find ways of reducing the error on the time and
energy of photon emission so each photon can be identical. Shown in Figure 2 is
a measurement where successive photons from one of our LEDs are collided on a
mirror, from opposite directions. The probability of the two photons leaving in
opposite directions falls when the photons arrive at identical times (reference
1). In this experiment the LED was operated in a pulsed mode at a rate of
500MHz. We have recently reported another experiment with the LED run on a DC
current, in which case interference can surprisingly still be observed if fast
enough detectors are used to make the measurements (reference 2).
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| Figure 2: A measurement of the probability of the two photons leaving in opposite directions (y-scale) as the time delay between the photons is changed (x-scale). When the photons arrive at the same time (1.98ns) is it impossible to tell which photon is which, and the interference occurs. |
References
[1] A. J. Bennett, R. B. Patel, A. J. Shields, P.
Atkinson, C. Nicoll, K. Cooper and D. A. Ritchie, Appl. Phys. Lett. 92
(2008) 193503.
[2] R. B. Patel, A. J. Bennett, A. J. Shields, P. Atkinson, C. Nicoll, K. Cooper
and D. A. Ritchie, Phys. Rev. Lett. 100 (2008) 207405.
A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
New Journal of Physics 10, 073013 (2009)
Miguel Navascués, Stefano Pironio and Antonio Acín
Overview
Consider a standard scenario in which two distant parties, Alice and Bob, perform m different measurements of n possible outcomes on their quantum systems. We denote by a,b=1,…,n the obtained results and by x,y=1,…,m the choices of measurement by Alice and Bob, see also Figure 1. The observed measurement statistics is described by the joint conditioned probability distributions P(a,b|x,y). The question we aim at answering is to characterize those correlations that can be obtained by quantum means. More precisely, given some correlations P(a,b|x,y), we want to know whether there exist a quantum state and measurements and b by Alice and Bob such that

The motivation for this problem is two-fold. First of all, from a fundamental point of view, we want to understand which correlations are possible within our current description of the microscopic world, given by Quantum Mechanics. Indeed, any result in this direction can be understood as the quantum analogue of Bell’s inequalities, which define constraints on correlations associated to the classical formalism. Second, from a Quantum Information point of view, identifying the limitations on correlations imposed by the quantum formalism improves our understanding of to which extent quantum resources are useful for information processing.
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Figure 1: Alice and Bob perform m different measurement of n possible results. The observed statistics is described by the conditioned probability distributions P(a,b|x,y). |
At first sight, the problem we face is quite
challenging, since we want to explore all possible quantum realizations of some
observed correlations. Therefore, it is very hard to give a precise
characterization of the set Q of correlations attainable by quantum means.
However, in a previous work [1], we introduced an infinite hierarchy of
conditions necessarily satisfied by any quantum correlation, that is,
probability distributions of the form (1). In more pictorial terms, these
conditions define different set of correlations which contain the actual quantum
set, see Figure 2. Moreover, each of these conditions could be tested using
semidefinite programming, which simplifies their numerical implementation.
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Figure 2: The derived hierarchy of conditions provides tighter approximations, γi, to the real quantum set Q. The hierarchy converges to Q in the limit i→∞. |
In the highlighted New Journal of Physics (NJP)
paper[2], we present new results concerning this hierarchy. We prove in
particular that it is complete, in the sense that any set of correlations
satisfying every condition in the hierarchy has a quantum representation in
terms of commuting measurements. This means that the corresponding set of
correlations give better and better, and asymptotically converging,
approximations to the real quantum set. Although the tests are conceived to rule
out non-quantum correlations, and can in principle certify that a set of
correlations is quantum only in the asymptotic limit where all tests are
satisfied, we also show that in some cases it is possible to conclude that a
given set of correlations is quantum after performing only a finite number of
tests. We provide a criterion to detect when such a situation arises, and
explain how to reconstruct the quantum states and measurement operators
reproducing the given correlations. Finally, we discuss several applications of
this approach, in particular to establish non-trivial upper bounds to the
quantum violation of Bell’s inequalities.
The same work [2] has recently been highlighted as one of the best NJP papers
published in 2008, see
http://www.iop.org/EJ/journal/-page=extra.bestof2008/1367-2630.
The results presented in [2] have been proven
independently by another research group [3].
References
[1] Miguel Navascués, Stefano Pironio and Antonio
Acín, Phys. Rev. Lett. 98, 010401 (2007).
[2] Miguel Navascués, Stefano Pironio and Antonio Acín, New J. Phys. 10, 073013
(2008).
[3] A.C. Doherty, Y. Liang, B. Toner and S. Wehner, arXiv:0803.4373.
January 2009
A high
bandwidth quantum repeater
Physical Review Letters 101, 040502 (2008)
W. J. Munro, R. Van Meter, Sebastien G. R. Louis, Kae Nemoto
Quantum information has reached a very interesting stage in its development,
where we have seen many fundamental experiments laying the foundation for
practical systems. Now certain applications, such as quantum key distribution (QKD),
are being readied for commercial use, where practical distances hover around the
150km mark. Any quantum communication longer than this limit suffers severely
from noise and exponential loss in the quantum communication channel. Hence, the
quantum communication for either QKD over a distance beyond the limit or, more
generally, all distributed quantum information processing, requires the
development of a high-bandwidth repeater which can distribute and potentially
process quantum information given these constraints. In a quantum repeater
system, initial imperfect Bell pairs (which we call base-level pairs) are
distributed over channel segments. These pairs are then purified to high
fidelity Bell pairs and connected via entanglement swapping, resulting in
entanglement between the qubits at distant stations. Iterating this procedure
creates Bell pairs at even larger distances. These pairs can be used in many
different applications, including QKD, quantum communication, distributed
quantum computation, and quantum metrology and related uses.
The many recently-proposed schemes for the design of a quantum repeater fall
into two categories. The majority of the schemes focus on the heralded creation
of very high fidelity base-level pairs [1]. For longer segment lengths, the
generation of these high fidelity pairs comes at the expense of a very low
probability of success, which becomes one of the major bottlenecks in the
overall performance of a repeater system. Another significant issue is that in
the majority of these schemes, local gates between multiple qubits within a
single repeater station are difficult. An alternative approach has recently been
proposed, instead creating base-level pairs of moderate fidelity and high
heralded success probability [2]. In this second approach, the physical
resources used for long-distance entanglement also efficiently implement local
gates, facilitating the purification of moderate fidelity pairs back to high
fidelity pairs. For instance with 16 qubits/node with a 10km spacing rate 15
pairs of fidelity F=0.98 can be achieved over a 1280km repeater network, however
at longer repeater node spacing distances (>40km) the rate fails to zero. This
node spacing issue is one of the key limitations for this second approach. These
two approaches are radically different in the use of physical resources and in
technological requirements. It is hence not trivial to directly compare the
feasibility and efficiency of schemes in different approaches. However, it has
been thought that these two approaches are complementary to each other, trading
high fidelity for high success probability or vice versa. Quantum repeaters of
the latter kind typically use coherent light instead of the single photons
common in the former category. It has been believed that a coherent-light
quantum repeater is fundamentally unable to generate high-fidelity Bell pairs
and hence is unable to cope with severe loss in the quantum channel. We have
addressed this shortcoming by presenting a design of a new scheme for
entanglement distribution utilizing coherent light (see Fig. 1) and demonstrated
that in fact such a system is more flexible over a wide range of losses without
serious overhead in physical resources. This advance will have a significant
impact on the overall repeater performance.
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| Figure 1: Schematic of an entanglement distribution scheme based on two qubits in individual cavities interacting indirectly via a shared probe beam and controlled displacement operations. An optical circulator before the second qubit routes the probe field into the cavity and then the probe beam leaking out of the cavity to the detector. A phase reference is sent along the same lossy channel. |
References
[1] See for instance H.-J. Briegel et al., Phys.
Rev. Lett. 81, 5932 (1998); W. Dur et al., Phys. Rev. A 59, 169
(1999); L. Childress et al., Phys. Rev. A 72, 052330 (2005); L. Childress
et al., Phys. Rev. Lett. 96, 070504 (2006); S. J. Enk et al., Science
279, 205 (1998); L.M.
Duan et al., Nature 414, 413 (2001); Z.-B. Chen et al., Phys. Rev. A
76, 022329 (2007)
[2] P. van Loock, Phys. Rev. Lett. 96, 240501 (2006)
Dephasing assisted transport: Quantum networks and biomolecules
| Dephasing assisted transport: Quantum networks and biomolecules New Journal of Physics 10, 113019 (2008) M.B. Plenio and S.F. Huelga |
Mechanisms for noise supported energy transfer in biological systems E-print arXiv:0901.4454 F. Caruso, A. Chin, A. Datta, S.F. Huelga and M.B. Plenio
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Overview
It has been recognized that the initial steps of natural photosynthesis harness the available light energy with almost unit efficiency (typical measured rates range from 95-99%). Despites decades of intense research, a clear understanding of the mechanisms behind this remarkably efficient transport process remain elusive [1]. Recently, experiments to probe the dynamics of delocalized exciton states in light-harvesting complexes and the Fenna-Metthew-Olson (FMO) complex provided direct evidence of the presence of quantum coherence between multiple chromophoric sites. This result has led to the suggestion of identifying quantum coherence as a likely cause for the highly efficient energy transfer in these systems [2]. The situation, however, appears to be more complicated, as illustrated by the fact that pure quantum mechanics cannot explain the observed transfer rates while current observations can be accounted for if coherent transport were to be supported by the presence of a certain level of dephasing noise [3,4].
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Figure 1: The FMO complex on the left is composed of 7 pigments that are loosely bound to form a complex. Excitons may enter the complex, e.g. site 6 (blue), and are then transported to site 3 (red) where energy is transferred to the reaction centre where chemical reactions are initiated. The r.h.s. depicts a simplified model of this complex where each pigment is represented as a single site and the interaction between sites is an excitation number preserving hopping term in a Hamiltonian. The exciton may be destroyed via spontaneous emission and the complex may suffer dephasing noise from a phonon bath (due to the many possible vibrational modes of the complex). |
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Figure 2: Increasing the level of dephasing leads to an increased success probability for transport of energy through the FMO complex. The noise free setting (solid line) leads to a transfer probability of ~50% while in the presence of an optimal dephasing rate this may rise to ~98% |
There are several processes that contribute to facilitate the dephasing assisted transport and these have been identified in [5]. The key observation is to realize that when an exciton enters the complex, it may explore different paths and hence experience constructive and destructive interference. Destructive interference closes off certain propagation channels and may in fact lead to population trapping due to cancellation of transition amplitudes. Dephasing noise inhibits this destructive interference and may as a result release trapped population (see fig 3a). Destructive interference depends on the existence of fixed phase relationships in the quantum state of the system and can therefore be affected by static disorder whereby different sites have different energies. This asymmetry leads to a time evolution of relative phases and thus the conversion from destructive to constructive interference (see fig. 3b). The latter is in striking difference to the destructive effect that static disorder plays in the process of Anderson localization. Finally, dephasing resulting from energy level fluctuations will enhance the overlap between neighbouring energy level and hence facilitate transport. The latter scenario may already be understood at a classical level, as illustrated in fig 3c., where initially forbidden transitions become possible when energy gaps are reduced.
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Figure 3 |
The discovery of dephasing assisted transport and the elucidation of the fundamental mechanisms that are leading to it opens up the road to better understanding the dynamics of photosynthetic complexes and may help us designing more efficient nano-scale devices for energy transport which could potentially lead to improved artificial light harvesting systems.
References
[1] Y.-C. Cheng and G.R. Fleming, Annu. Rev.
Phys. Chem. 60, 241 (2009)
[2] G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng,
R. E. Blankenship, and G. R. Fleming, Nature 446, 782 (2007).
[3] M. B. Plenio and S. F. Huelga, New J. Phys 10, 113019 (2008)
[4] M. Mohseni, P. Rebentrost, S. Lloyd, and A. Aspuru-Guzik, J. Chem. Phys 129,
174106 (2008); P. Rebentrost, M. Mohseni, and A. Aspuru-Guzik, arxiv:0806.4725
(2008); P. Rebentrost, M. Mohseni, I. Kassal, S. Lloyd, and A. Aspuru-Guzik,
arxiv:0807.0929 (2008).
[5] F. Caruso, A. Chin, A. Datta, S.F. Huelga and M.B. Plenio, E-print
arXiv:0901.
December 2008
A Solid-State Light-Matter Interface at the single photon level
Nature 456, 773 (2008)
Hugues de Riedmatten, Mikael Afzelius, Matthias U. Staudt, Christoph Simon
and Nicolas Gisin
QAP researchers from the University of Geneva have demonstrated a storage device
for photons in a solid state environment. This technique enables the coherent
and reversible transfer of quantum information between light and a solid state
system, which provides a promising tool for the realization of quantum repeaters
and quantum networks.
Coherent and reversible mapping of quantum information between light and matter
is an important experimental challenge in quantum information science. In
particular, it is an essential requirement for the implementation of quantum
networks and quantum repeaters. Up to now, experiments in photonic quantum
storage have been performed with atomic gases or single atoms in cavities. In a
recent Nature paper, QAP researchers from the University of Geneva report the
coherent and reversible mapping of a light field with less than one photon per
pulse on average onto an ensemble of 107 Neodymium atoms naturally trapped in a
solid, cooled at 3 K.
In order to achieve the mapping, the authors take advantage of the inhomogeneous
broadening of the optical transition of the Nd atoms. By optically pumping some
of the atoms out of the ground state, the absorption spectrum is tailored with a
series of periodic narrow peaks, an atomic frequency comb. The weak incident
light field is collectively absorbed by all the atoms in the comb, and the state
of the light is transferred to collective atomic excitations at the optical
transition. After absorption, the atoms at different frequencies will dephase,
but thanks to the periodic structure of the absorption profile, a rephasing will
occur after a time which depends on the comb spacing (up to 1
µs in the present experiment). When the
atoms are all in phase again, the light is re-emitted in the forward direction
as a result of a collective interference between all the emitters.
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Figure 1. Picture of the crystal containing Nd impurities. |
In the actual experiment, the storage and retrieval efficiency is low (about 1 %), mainly because of imperfect preparation of the atomic frequency comb. Much higher efficiencies (which in theory can go up to unity) should be however readily achieved with simple improvements of the experiment. Despite the low efficiency, the quantum coherence of the incident weak light field is almost perfectly conserved during the storage, as demonstrated by performing an interference experiment with a stored time-bin qubit. The researchers also demonstrate experimentally that the interface makes it possible to store light in multiple temporal modes (See Fig 2). This last feature is particularly interesting, as it enables temporal multiplexing in future quantum repeaters architectures.
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| Figure 2: Storage and retrieval of weak light pulses in single (left) and multiple (right) temporal modes | |
How many classical resources are needed to simulate quantum measurements?
Physical Review Letters 101, 190402 (2008)
B. Dakic, M. Šuvakov, T. Paterek, and C. Brukner
Overview
The question from the title is relevant if one wants to make a fair
comparison between complexities of quantum and classical algorithms. It was
previously known that the results of a finite set of general quantum
measurements on an arbitrary dimensional quantum system can be simulated using
an exponential (in measurements) number of "hidden-variable" (classical) states.
In Physical Review Letter 101, 190402 (2008), Dakic, Suvakov, Paterek and
Brukner, have constructed an explicit model in which the number of
hidden-variable (HV) states scales polynomially with the number of quantum
measurements, thus bringing an exponential improvement. In addition to the
relevance for quantum information science the work is motivated by a fundamental
question.
John Bell showed that it is impossible to explain all of the predictions of
quantum mechanics using a theory which still satisfies the basic concepts of
locality and realism, but which (if not both) is violated is still an open
question. Dakic et al. ask how plausible realism -- the idea that external
reality exists prior to and independent of observations -- is, by considering
the amount of resources in terms of the number of HV states realism consumes. In
the limit of large number of measurements, the model of Dakic et. al confirms
the result of Montina, that no successful realistic theory could use less HV
states than the one in which every quantum state is associated with a HV. This
shows that, for any given system size, realistic theories cannot describe nature
more efficiently than quantum theory itself. The paper extends the work of
Hardy, who showed that, even for the simplest quantum system like electron spin
or photon polarisation, realism is extremely resource demanding, requiring
infinitely many HV states to explain all possible measurements.
Editor’s Reading Suggestion
A. Montina, Phys. Rev. A 77, 022104 (2008).
L. Hardy, Stud. Hist. Philos. Mod. Phys. 35, 267 (2004).
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Figure 1: Hidden-variable (HV) models for quantum measurements (a) The vertices of the octahedron inside the Bloch sphere define the three complementary qubit measurements. A HV model for these measurements for arbitrary quantum state requires eight HV states, which are written near their representative vertices of the cube containing the sphere.(b) Here, the measurement directions form a cube inside the sphere. Although more measurements are to be simulated, the universal HV model requires only six HV states, which are written near their representative vertices of the octahedron containing the sphere. |
October 2008
Multipartite Entanglement Among Single Spins in Diamond
Science 320, 1326 (2008)
P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V.
Jacques, T. Gaebel, F. Jelezko, J. Wrachtrup
Since Entanglement of quantum states is a benefit or even a
prerequisite for quantum information protocols, proving this for a candidate
system is a necessary benchmark. In the case of a single Nitrogen-Vacancy (NV)
center in diamond we have demonstrated entanglement among its electron spin and
two adjacent nuclear spins of the 13C isotope coupled via their
hyperfine interaction. Due to the almost spinless and stiff diamond lattice it
was possible to perform these experiments under ambient conditions without
suffering the loss of coherence due to e.g. lattice phonons. Some quantum
correlations even persist on a millisecond timescale.
The NV center in diamond consists of a nitrogen atom at one lattice site and a vacancy on a neighbouring lattice site (fig. 1a). Since its negatively charged version has a spin triplet ground state a qubit can be encoded among two of these ground state levels e.g. mS=0 → “0”, mS=-1 → “1”. The defect center shows very strong fluorescence in the red when excited with green laser light which allows us to investigate single centers with a confocal microscope. Moreover the fluorescence depends on the electronic spin state making it possible to read out the electron spin optically. Finally by laser excitation the NV center can be polarized in one of its spin triplet levels in the ground state (namely mS=0 (“0”)). This serves as initialization of our system. Coherent transitions between spin levels in the ground state are mediated via microwave radiation.
In the present center two of the closest carbon atoms are
13C isotopes with nuclear spin ½ which serve as additional qubits. Their
strong hyperfine coupling to the electron spin of the NV center allows us to
address and manipulate the nuclear spins individually by applying appropriate
radiofrequencies (fig. 1b,c).
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Figure 1: (a) structure of the NV center in the diamond lattice. Two of the three nearest neighbor carbon atoms are 13C isotopes with nuclear spin ½ in this case. The other one is spinless 12C isotope. (b) Energy levels of this NV center showing the mS=0 and -1 branch with hyperfine splitting due to the 13C atoms. Blue arrows show electron spin transitions and the orange ones nuclear spin transitions. (c) Electron spin resonance spectrum showing all four transitions shown in panel b. |
After initializing the system with a laser pulse our coherent control of the electron and nuclear spins allows us to generate and read out all 4 Bell States among the 2 nuclear spins (fig. 2a,b). These are the maximally entangled states among 2 qubits. In short, the outstanding property of these Bell states are that effective one particle measurements allow to determine the state of the other qubit with certainty. The entanglement lasts for a few milliseconds where the measurement is limited by the electron spin’s T1 time. That is until the spin starts to change its state randomly between “0” and “1”. The existence of a Bell state can be proven by Ramsey fringes (fig. 2a) which show the evolution of the Bell state or by performing a tomography. The resulting tomogram (fig. 2b) shows the expected correlations on its off-diagonal elements (|00><11|, |11><00|).
Taking into account also the electron spin 3-partite entangled states have been created. That is the so called GHZ (Greenberger-Horne-Zeilinger) state and the W state. Similar to the Bell states a measurement of one qubit of a GHZ state determines the state of the remaining 2 qubits. While for the W state depending on the measurement result the remaining qubits are either determined or still entangled among each other. A tomogram (fig. 2c) reveals these correlations on all respective off-diagonal elements.
With this 3 qubit system at hand first quantum algorithms can be tested, e.g. “superdense coding” or the “Deutsch algorithm”. Further scaling up of the system requires additional nuclear or electron spins close to the NV or the coupling of several NV centers by magnetic dipole interaction or by probabilistic entanglement via photons.
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Figure 2: (a) These Ramsey fringes show the free evolution of the generated Bell states F+, F-, Y+ and Y-. This is a prove for their generation. (b) To obtain this tomogram of the state F- all 16 density matrix elements have to measured. Especially the negative columns on the off-diagonal prove the Bell state. (c) Partial tomogram of the W state showing its off-diagonal elements. |
Coherent Control of Decoherence
Science 320, 638 (2008)
Matthijs P. A. Branderhorst, Pablo Londero, Piotr Wasylczyk, Constantin Brif, Robert L. Kosut, Herschel Rabitz, Ian A. Walmsley
Overview
QAP researchers have found a way of protecting quantum systems against noise using adaptively ‘shaped’ pulses of laser light. Quantum systems are notoriously fragile as interactions with their surroundings disturb them – rather like an orchestra trying to stay in tune in a very noisy environment. However, maintaining the stability of quantum systems is critical for future quantum technologies. In a recent Science paper, researchers at the University of Oxford report that they have found a way to prolong the life of a model quantum system.
The advance used light pulses, with a colour spectrum shaped in amplitude and phase, to control the dynamics of the model quantum system. Using a genetic algorithm, the researchers were able to find the optimal pulse shape to protect the system from decay. Contrary to what might be expected, the encoded order from the light pulse makes the quantum system more robust against disorder.
Matthijs Branderhorst, who did the experiment, explained: ‘There have been control techniques before to improve stability but they rely on knowing everything about a given system. The ground-breaking nature of our approach is that, knowing nothing about a system, we can automatically search for and apply a light pulse that makes it more robust. We have shown an improvement of the stability with our experimental test system, but in other cases it could make it completely immune from decay.’
The model system used by the researchers to study the idea consisted of two
potassium atoms bound together. However, the approach they have developed could
be applied to many other kinds of quantum systems such as those influencing
chemical reactions, photosynthesis and quantum computation.
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Figure 1: The laser oscillator used to generate light pulses for adaptive coherent control of potassium dimers. Such a laser system could be used to protect the stability of future quantum technologies. |
Septemeber 2008
QLib
Shai Machnes
QLib is an open-source Matlab package intended to provide everybody within the
Quantum Information community with a comprehensive toolset, and to allow us to
- Quickly and efficiently frame and explore ideas
- Form intuition through the use of visualizations
- Rule-out or validate hypothesis through the use of optimization
QLib currently covers most, if not all, of the "textbook" primitives and provides us with a rich toolset with which to advance knowledge in out field and engage in "experimental theory".
On the QLib site you will find everything you need: the software itself, a “getting started” guide, examples, forums to ask questions, report bugs and request features – everything necessary to get you up and running as quickly as possible.
QLib is free to use and modify, and is licensed under the GPL. Our goal is to have QLib continually developed by the community and for the community, to the benefit of us all.
Further details about QLib can be found in the pdf document below, or at the QLib website.
QLib summary document, © Shai Machnes, Tel-Aviv University
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Scaling Laws for the Decay of Multiqubit Entanglement
Physical Review Letters 100, 080501 (2008)
L. Aolita, R. Chaves, D. Cavalcanti, A. Acin, and L. Davidovich
Overview
In most cases the speed-up gained when using quantum-mechanical systems, instead of classical ones, to process information is only considerable in the limit of large-scale information processing. Within such context, it is therefore fundamental to understand the scaling properties of disentanglement for multi-particle systems. With this aim, Simon and Kempe showed [1] in 2002 that the genuinely multiparticle-entangled Greenberger-Horne-Zeilinger (GHZ) states,
subject to the action of individual depolarization, undergo entanglement sudden death (ESD), that the last bipartitions to loose entanglement are the most balanced ones, and that the time at which such entanglement disappears grows with the number of particles in the system. Soon afterwards it was shown by Dür and Briegel [2] that the first N bipartitions to loose entanglement are the least balanced ones (one particle vs. the others), the time at which this happens decreasing with . A natural question arises from these considerations: is the ESD time a truly physically-relevant quantity to assess the robustness of multi-particle entanglement?
In this highlighted paper, the QAP researchers have shown that, for an important family of genuine multipartite entangled states - namely the generalized GHZ states
, the answer is no.
For several paradigmatic models of decoherence, they have derived analytical expressions for the time of disappearance of entanglement, which is found to increase with N. However, they have shown that the time at which entanglement becomes arbitrarily small decreases with the number of particles, independently of ESD. This implies that for multi-particle systems, the amount of entanglement can become too small for any practical application long before it vanishes. The situation is exemplified in Fig. 1, where the entanglement (quantified by the negativity) of the most robust bipartitions is plotted versus the probability p of depolarization due to the interaction with the environment, for generalized GHZ states of α =1/3 and β=√8/3, of systems of 4, 40 and 400 two-level particles (qubits). Even though the 40-qubit and 400-qubit negativities cross the 4-qubit one and vanish much later, they become orders of magnitude smaller than their initial value - and therefore negligible for all practical purposes - long before reaching the crossing point. This same behaviour is also found for all other parameters and maps.
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| Fig. 1: Negativity versus probability p of depolarization for N=4, 40 and 400 and for the most balanced partitions, which are the last ones to loose their entanglement. The inset shows a magnification of the region in which the four-qubit system’s negativity vanishes. Even though the other two negativities cross the latter and vanish much later, they become orders of magnitude smaller than their initial value long before reaching the crossing point. |
As a by product, the researchers have also shown that in several cases the action of the environment can naturally lead to multi-particle bound (non-distillable) entangled states, in the sense that, for a period of time, it is not possible to extract pure-state entanglement from the system
through local operations and classical communication, even though the state is still entangled. This, in view of the lack of a general recipe for the creation of bound entanglement, is very interesting because it means that, despite its detrimental action on quantum correlations, the environment can effectively act as a generator of this very mysterious form of entanglement (See Fig. 2).
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| Fig. 2: Negativity as a function of p for a four-qubit GHZ (α = 1/√2 = β) state and independent depolarizing channels again. After the 1:3 negativities vanish (all four of them vanish together) no pure-state entanglement can be extracted from the state through local operations even with the assistance of classical communication. Nevertheless, the state is still entangled, as witnessed by the negativities of the balanced 2:2 partitions. |
Concluding, the time at which entanglement becomes arbitrarily small characterizes better the robustness of the states’ entanglement than the time at which entanglement death itself occurs; and in several cases the action of the environment can naturally lead to bound entangled states. Finally, this work establishes a new venue for future research: in a forthcoming work, for example, the researchers will show that it is indeed possible to extend these results to other quantifiers of entanglement apart from the negativity. And also open questions are left: how do other genuinely multipartite entangled states, such as graph states, or matrix-product states behave? W states on the other hand are expected to be more robust, since they have always only one excitation, regardless of N, as will also be shown in forthcoming work by the same authors. Nevertheless, the results already obtained suggest that maintaining a significant amount of multi-qubit entanglement in macroscopic systems might be an even harder task than believed so far.
July 2008
Cryptography from Noisy Storage
Physical Review Letters 100, 220502 (2008)
Stephanie Wehner, Christian Schaffner and Barbara M. Terhal
With the arrival of widespread electronic communication new cryptographic tasks
have become increasingly important. We are no longer satisfied with the secure
and reliable transmissions of messages, but want to solve a large number of
tasks where the protocol participants themselves do not trust each other.
Important examples of such tasks are secure identification, electronic voting,
and contract signing. Unfortunately, it has been shown that it is impossible to
implement such tasks securely without making assumptions on how powerful an
attacker can be, even if we allow quantum communication. Classically a commonly
used assumption is that it is difficult to factor a large number. This
assumption, however, no longer holds once a quantum computer is built, and it is
presently unknown whether this assumptions even holds classically. It is
therefore an important problem to find realistic assumptions that allows us to
achieve such tasks. Can quantum communication be of any help us?
Recently, it has been shown by QAP researchers that we can implement two-party
protocols securely if we assume that it is difficult to store quantum states
without errors. Here, the very problem that makes it so hard to implement a
quantum computer can actually be turned to our advantage. Practically, such
noise can arise as a result of transferring a photonic qubit onto a different
physical carrier, such as for example an atomic ensemble or atomic state. In
addition, a quantum state will undergo noise once it has been transferred into
'storage' if such quantum memory is not 100% reliable.
As a proof of principle, the QAP researchers have shown that we can obtain the
two-party protocol 1-out-of-2 oblivious transfer in this model. This important
primitive, that may indeed appear rather bizarre at first glance, can actually
be used as a fundamental building block to implement any two party protocol. In
oblivious transfer (see Figure 1), Alice holds two input bits s0 and
s1. The goal of the protocol is to allow Bob to retrieve one of the
two bits sc according to his choice bit c, in such a way that Alice
cannot learn which of the two bits Bob has retrieved. Thus, Bob cannot simply
ask for one of the bits. At the same time, the protocol should guarantee that
Bob can only learn exactly one of the two bits. Hence, Alice cannot simply send
her two inputs to Bob. In their work, the QAP researchers have examined a simple
protocol for this task, that can be implemented using hardware that is already
used today to implement quantum key distribution (QKD). No quantum storage is
thereby required for the honest participants. The key idea behind the protocol
is to show that if Bob is dishonest (that is he tries to learn more than one of
Alice's inputs) and attempts to store the quantum states sent by Alice until
maybe later he received some additional information that would help him, he has
already lost too much information due to the noise in the storage process. (see
Figure 2)
In a real world setting, the honest players Alice and Bob do of course also
experience some noise in their operations. In more recent work (arxiv:0807.1333)
however it was shown that the protocol for oblivious transfer still remains
secure, even if the honest participants experience 11% of noise and the noise on
the channel and in their operations is strictly less than the noise in the
quantum storage. This value may seem small, but unlike QKD, it is still
interesting to implement such protocols even over very short distances. This is
particularly the case for secure identification that is of relevance to banking
applications.
This work shows that noise can indeed sometimes be a good thing and help us to
implement cryptographic primitives which are otherwise impossible to obtain
without making any assumptions. It opens the door for much further research in
this direction. Can we find efficient protocols for other tasks? (without using
the primitive oblivious transfer) What security to we obtain from more
generalized noise models than the ones considered here? Finally, what are the
fundamental limits of this model?
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Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source
Physical Review Letters 100, 090501 (2008)
Q. Wang, W. Chen, G. Xavier, M. Swillo, S. Sauge, M. Tengner, T. Zhang, Z. F. Han, G. C. Guo, A. Karlsson
Overview
Using an optimized heralded single-photon source (HSPS) based on parametric down-conversion, the KTH research group cooperating with a Chinese USTC group has experimentally demonstrated a decoy-state quantum key distribution scheme (QKD) [1-3]. They used a one-way BB84 protocol with a four states and one-detector phase-coding scheme, which is immune to recently proposed time-shift attacks, photon-number splitting attacks, and can also be proven to be secure against Trojan horse attacks and any other standard individual or coherent attacks.
As shown in Fig. 1 (below), using the BB84 protocol and under the same
experimental conditions, we compare our HSPS with decoy state scheme to several
other schemes, including HSPS without decoy states,
weak coherent state (WCS) with or without decoy states, and also the ideal
single-photon source (SPS) case. (In order to give a fair comparison, all these
lines are not taken statistical error into account.) As can be seen, our scheme
(red solid line) gets the maximum tolerable losses or the highest key generation
rate under fixed losses among all these practical schemes. Moreover, if a better
HSPS (blue dashed line with 70% correlated photon pairs) is used, its
performance comes close to the ideal single-photon source.
Our experimental setup is shown in Fig. 2, and our final experimental results
fit our theoretical predictions [4] quite well as shown in Fig. 3.
However, our final key rate is lower than in other systems reported before, because there are large losses in our QKD system. With present technology, it is realistic to decrease the loss by 15 - 18 dB in this QKD system, which is quite considerable for a long distance transmission (>100 km).
Despite of these deficiencies in our present system, this experiment is still sufficient to prove, in principle, that our HSPS based decoy-state scheme can tolerate the highest losses among all practical schemes, which also means the highest secure key generation rate under fixed losses. Therefore, it is a good candidate for future quantum key distribution systems.
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Fig.1. The key generation rate vs. the total losses comparing several different schemes. The numerical simulations are done in the case of: a) with WCS and without decoy-state method; b). with HSPS and without decoy-state method; c). with WCS based decoy-state method (with optimal values of signal intensity at each points and an infinite number of decoy states); d). with HSPS based decoy-state method with Pcor=30%; e). with HSPS based decoy-state method with Pcor=70%; f). with the ideal SPS. |
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Fig.2. The experimental setup of the quantum key transmission system: PPLN: periodically-poled LiNbO3, AOM: acousto-optical-modulator, WDM: wavelength-division multiplexing, OS: optical switch, TC: time chopper, BS: beam-splitter, FM: Faraday Mirror, PM: phase modulator, DL: delay line, QC: quantum channel, SPD: single photon detector, CB: control board. |
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Fig. 3. The top line represents the theoretical counting rate for signal photons; the bottom line represents the theoretical secure key rate (taking statistical fluctuation into account). For each line, we investigated two points at the total loss of 31dB and 36dB individually. The stars and triangles are corresponding experimental results. |
References
[1] W. Y. Hwang, Phys. Rev. Lett. 91, 057901 (2003).
[2] X. B. Wang, Phys. Rev. Lett. 94, 230503 (2005).
[3] H. K. Lo, X. Ma, and K. Chen, Phys. Rev. Lett. 94. 230504 (2005).
[4] Q. Wang et al. ArXiv: quant-ph/0803.3643
June 2008
QAP researcher wins prize for outstanding research!
Congratulations to Dr. Christine Silberhorn for winning the prestigious Heinz Maier-Leibnitz Prize 2008. Dr. Silberhorn is one of 6 young researchers to be recognised by German Research Foundation for outstanding contributions to science. The Prize has been awarded to young researchers annually since 1977 to promote the further development of outstanding independent profiles. The prize of €16,000 is simultaneously a form of recognition of past achievements and an incentive to continue climbing the scientific career ladder. As such, it is held in high regard by the whole scientific community. Dr. Silberhorn's citation for the award is included below.
Christine Silberhorn's research to date is characterised by an extremely broad range of interests and research topics as well as a wide variety of international experience, and she has attained a very good reputation in the field of experimental quantum optics within the period of just a few years. During her studies she was already interested in highly abstract topics relating to topology, before moving on to the entirely different area of quantum cryptography for her PhD thesis. She has been able to establish herself very well in the rapidly progressing and thus highly competitive research field of quantum information processing. Her main area of interest was how to process and transmit quantum information using light, an issue that is of key importance for any quantum computers that may be built in the future. Instead of the discrete variables normally employed, Silberhorn used so-called "continuous variables", thus developing a widely accepted alternative. Silberhorn is currently continuing this work as the leader of an independent Max Planck junior research group, in which she, herself still a young scientist, is combining her successful research work with the opportunity to train other young researchers and scientists.
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Figure 1: Dr. Christine Silberhorn (Front, second left) pictured with other winners of the Heinz Maier-Leibnitz Prize 2008. |
Superconducting Nanowire Photon Number Resolving Detector at Telecom Wavelength
Nature Photonics 2, 302 - 306 (2008)
Francesco Marsili, David Bitauld, Aleksander Divochiy, Alessandro Gaggero, Roberto Leoni, Francesco Mattioli, Alexander Korneev, Vitaliy Seleznev, Nataliya Kaurova, Olga Minaeva, Gregory Gol’tsman, Konstantinos G. Lagoudakis, Moushab Benkhaoul, Francis Lévy, Andrea Fiore
Overview
The characterisation of photon number states is an essential tool in photonic quantum information processing, however existing photon-number resolving (PNR) detectors are either too noisy or too slow for practical applications. QAP researchers recently demonstrated a PNR detector, the Parallel Nanowire Detector (PND) [1], which uses spatial multiplexing on a subwavelength scale to provide a single electrical output proportional to the photon number. The basic structure of the PND is the parallel connection of superconducting nanowires (N-PND). The detecting element is a few nm-thick, ~100 nm-wide NbN wire folded in a meander pattern (fig. 2a), which can be integrated in series with a bias resistors R0 (N-PND-R) (fig. 2b). Each branch acts as a superconducting single photon detector (SSPD) [2]. If a superconducting nanowire is biased close to its critical current, the absorption of a photon causes the formation of a normal barrier across its cross section and the bias current is pushed to the external circuit. In the parallel configuration proposed here, the currents from different wires can sum up on the external load, producing an output voltage pulse proportional to the number of photons. The integration of the resistance R0 improves the performance of the device in terms of speed and stability of operation [3].
PNDs were fabricated on ultrathin NbN films (4nm) on MgO [4] and R-plane
sapphire [5] using electron beam lithography (EBL) and reactive ion etching. The
photoresponse pulse is as short as 660ps (full width at half maximum). Counting
performance was observed up to 80 MHz repetition rate. Building the histograms
of the photoresponse peak (fig. 3), no multiplication noise is observable and
the one photon quantum efficiency can be estimated to be 3% (at 700 nm
wavelength and 4.2 K temperature). The PND thus significantly outperforms
existing PNR detectors in terms of simplicity, sensitivity, speed, and
multiplication noise.
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Figure 2. Scanning electron microscope (SEM) images of a 14-PND (a) and a 8-PND-R (b) fabricated on a 4 nm thick NbN film on MgO. The nanowire width is w=100 nm, the meander fill factor is f=40%. In fig. (b) the active nanowires (in color) are connected in series with Au-Pd bias resistors (in blue). |
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Figure 3. Photoresponse transients of a 10x10 μm2 6-PND-R (□) probed at 5 K under illumination with 1.3 μm pulses from a laser diode, at a repetition rate of 26MHz. The red solid curves are guides to the eyes. The histogram of the photoresponse voltage peak is shown on the left hand side of the picture in turquoise. |
References
[1] A. Divochiy et al., Nature Photon. 2, 302 (2008).
[2] G. N. Gol'tsman et al., Appl. Phys. Lett. 79, 705 (2001).
[3] F. Marsili et al., J. Mod. Opt. to be published.
[4] F. Marsili et al., Opt. Express 16, 3191 (2008).
[5] G. N. Gol'tsman et al., IEEE Trans. Appl. Supercond. 13, 192 (2003).
May 2008
Migration of bosonic particles across a Mott insulator to superfluid phase interface
Physical Review Letters 100, 070602 (2008)
Michael J. Hartmann and Martin B. Plenio
Overview
Quantum many body systems are, in the forms in which they occur in nature,
difficult to study experimentally. These difficulties lead to the development of
quantum simulators with which many body effects can be emulated in the
laboratory. Recent approaches to quantum simulators now give rise to
possibilities for engineering deliberate inhomogeneities in quantum many body
systems. This development could allow for the observation of dynamics at the
boundary between two areas of a many body system which are in different
condensed matter phases.
Recent work by QAP researches studies this dynamics theoretically and finds rather surprising effects. The scientists consider a boundary between a Mott insulator in which mutual particle repulsion strongly suppresses particle movement and an area in a superfluid phase, where particles do only interact very little an move almost freely and frictionless. The work by the QAP researchers shows that, in such a situation, all particles will leave the Mott insulator part and migrate to the superfluid region, leaving the Mott insulator part completely empty. Understanding and hence being able to control and make use of such effects is an important step towards the objectives of QAP.
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Figure 1: Migration of particles from a Mott insulator to a superfluid. The plot shows particle densities (nj) for a chain of 40 sites as a function of time (t). Initially the particle densities are 1 in both parts of the chain. They drop to zero in the Mott insulator part (sites 1 - 20) and grow in the superfluid part (sites 21 - 40) |
Exact Relaxation in a Class of Nonequilibrium Quantum Lattice Systems
Physical Review Letters 100, 030602 (2008)
M. Cramer, C. M. Dawson, J. Eisert, and T. J. Osborne
Open systems dynamics in closed quantum systems: Exact relaxation in quenched quantum many-body systems
Why do systems dynamically relax to a
statistical equilibrium state? This intriguing but old question is enjoying a
renaissance recently. With new experimental techniques becoming available, the
non-equilibrium dynamics of atoms in optical lattices can be experimentally
observed. Specifically, following a quench - that is, a rapid change of the
system's parameters - the many-body system undergoes complicated dynamics. So
what happens? There is no environment, so how could it possibly relax?
Recent work by QAP researchers published in the Physical Review Letters answers
this question rigorously for a class of models that are idealized instances of
the Bose-Hubbard model that takes centre stage in this discussion of atoms in
optical lattices. The authors demonstrate that while the information on the
initial condition is of course stored in the system at all times, it becomes
diluted with time. Locally, for any subsystem, one obtains a maximally entropy
state compatible with the constants of motion. Remarkably, this is true without
a time average: The system just smoothly and nicely relaxes. So when locally
looking at the system, we think that the system has reached its equilibrium. But
only apparently so, as one day, arbitrarily far in the future, a recurrence will
show that all the time, the initial condition was not forgotten.
This work discusses a scenario in which the dynamics of quantum phase
transitions in quantum many-body systems can be studied in experiments, in an
instance of a quantum simulation of a complex non-equilibrium process. The ideas
put forth on the simulation and quantum control of such a quantum man-body
system are very much inline with the objectives of QAP.
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Figure 2: Intuitive
picture of the relaxation process in the quenched Bose-Hubbard model:
For any lattice site i (or any block |
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Figure 3: Local density of particles as a function of time, for a periodic initial condition of atoms in an optical lattice, including an harmonic trap. This plot shows signatures of local relaxation. |
March 2008
Heralded Generation of Ultrafast Single Photons in Pure Quantum States
Physical Review Letters, 100, 133601 (2008)
Peter J. Mosley, Jeff S. Lundeen, Brian J. Smith, Piotr Wasylczyk, Alfred B. U'Ren, Christine Silberhorn, Ian A. Walmsley
Overview
Single photons (discrete wavepackets of light) are not only interesting in terms of fundamental physics, but also from the point of view of applications in the emerging field of quantum information processing - a field that has the potential to revolutionize computing by harnessing the data processing power inherent in quantum mechanics. In this paper, researchers at the University of Oxford present the results of a new technique, based on photon pair generation, that for the first time allows the preparation of single photons of exceptionally high quality, conditioned on the detection of their twin. Furthermore, these photons have a temporal duration of as little as 65 femtoseconds (65 millionths of a billionth of a second), believed to be the shortest single photons ever generated. The precise timing and consistent attributes of these photons make them ideal for implementing photonic quantum logic gates and conducting experiments requiring large numbers of single photons, as required by quantum computing algorithms.
The source is based on the process of parametric downconversion in nonlinear optical crystals. In a single downconversion event, one "parent" photon is destroyed, and two "daughter" photons of lower energy are created (see Figure 1). Downconversion is a commonly used method for generating photon pairs, with the detection of one daughter photon heralding the arrival of the second daughter photon. This simple detection arrangement makes downconversion an attractive prospect for generating the single photons required by many quantum information processing protocols. However, the detection of the herald photon usually ruins the quality (or purity) of the second daughter photon. Energy and momentum conservation in the generation process generally result in strong quantum correlations within each pair (known as entanglement). Upon detection of one photon, the possibility of obtaining distinguishing information about the other photon ruins the purity of its quantum state. Some experiments have countered this problem by spectrally filtering the photons, effectively throwing away the unwanted photons. Unfortunately this process greatly reduces the efficiency of the source, and the purity of the daughter photons only becomes 100% in the limit that all photons are filtered out!
In the work highlighted here, QAP researchers at Oxford have built a source which requires no filtering of the daughter photons but still delivers photons of excellent purity and with a high efficiency. By carefully controlling the parameters which dictate the momentum conservation in the downconversion process, Mosely et al. were able to engineer a source in which detection of one daughter photon does not automatically destroy the purity of the second daughter photon. The purity of the daughter photons was tested by constructing two identical downconversion sources and then combining the heralded daughter photons on a 50:50 beamsplitter (see Figure 1). If the photons from each source are of high quality and are therefore indistinguishable, they will bunch together at the beamsplitter and exit in the same direction: this is the Hong-Ou-Mandel effect. The plot in Figure 1 shows that when the heralded photons from each source reach the beamsplitter at the same time, the number of coincidences between the four detectors drops off dramatically due to this bunching effect. The dip measured in this work indicates that the photons have a purity of over 95%, generated with a high efficiency. This work will be a substantial benefit for future quantum information processing applications requiring high purity photons as it has eliminated the need for lossy spectral filters.
The Oxford group are now using such sources for quantum enhanced precision metrology, heralded entanglement generation and linear optical quantum computation schemes.
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Figure1: Scheme of the high purity photon pair
generation by parametric downconversion. |
Nonclassical Interference and Entanglement Generation Using a Photonic Crystal Fiber Pair Photon Source
Physical Review Letters, 99, 120501 (2007)
Jérémie Fulconis, Olivier Alibart, Jeremy L. O'Brien, William J. Wadsworth, and John G. Rarity
The scaling of linear optical networks to many qubits is currently limited by
the lack of bright single photon sources. Researchers at the University of
Bristol, in collaboration with the University of Bath have developed a versatile
solution based on photonic crystal fibres. Their work reports on the suitability
of these new fibre sources for optical quantum information processing.
Standard pair photon sources usually relied on spontaneous parametric
downconversion where the practical limit to multiphoton experiment is five or
six photons due to a high pump power requirement (typically a few Watts). Using
photonic crystal fibres, a pair of pump photons produces a correlated pair of
photons at widely spaced wavelengths, via a χ(3)
four-wave mixing process. The confined geometry of the fibre enhances the
non-linear interaction and the required average photon number per pulse is
reached at milliWatt pump powers.
Two key experiments are reported. The demonstration of high visibility
nonclassical interference between heralded photons from separate fibre sources
and high fidelity entangled photon pair generation by configuring the fibre in a
Sagnac loop interferometer. The photons are created within a single fibre mode
which can be efficiently coupled into linear optics circuits and on to
detectors. This source promises much higher rates of multiphoton generation than
conventional sources. This will open the way to a variety of novel experiments
including cascaded linear gates, or building large entangled cluster states,
which is inline with the objectives of the QAP project.
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Figure1: Scheme of the non-classical interference
setup (left) and entanglement generation (right). |
October 2007
Entangling independent photons by time measurement
Nature Physics, 3, 692 (2007)
Matthaus Halder, Alexios Beveratos, Nicolas Gisin, Valerio Scarani, Christoph Simon and Hugo Zbinden
Overview
Researchers in the Group of Applied Physics (GAP) at Geneva University have demonstrated an entanglement swapping experiment with autonomous sources. Normally, entanglement between two photons is produced by emitting them simultaneously from the same source. In this experiment the researchers show that entanglement can be transferred (or "swapped") on two photons, originating from autonomous sources and hence formerly completely independent. This is the first time that two autonomous photons have been entangled.
The scheme of Entanglement Swapping allows entangling photons, which have
been emitted by independent processes in remote sources (A and B, Fig. 1). Each
source emits a pair of entangled photons (A1-A2 and B1-B2, respectively). By
taking one photon from each pair (A1 and B1) and performing a joint measurement
(Bell state measurement, BSM), they are detected in an entangled state, one of
the four Bell states. For a successful outcome of the BSM, A2 and B2 are
projected onto an entangled state as well, even though they never interacted or
share any common past.
To enable a BSM, the photons A1 and B1 must be indistinguishable, which means in
particular, arrive at the same time at the beam splitter BS. Until now, this was
achieved by the use of pulsed sources with synchronized emission times and
matched fiber lengths. This is the first demonstration that precise timing of
photons at telecom wavelength can be achieved by detection and postselection. To
make this possible, the photons’ coherence length has to exceed the detectors
temporal resolution. Single photon detectors based on superconductors and
semiconductors, featuring a timing resolution of 70-100ps. By narrowly filtering
(10pm) the photons, their coherence length is increased to the order of 300ps.
Thus no synchronization between the sources is required anymore which makes them
truly autonomous.
This setup is compatible with some of the quantum memories currently under development in project QAP, because the source and memory bandwidths are within the same order of magnitude. The work is thus an important step towards quantum repeaters, one of the main QAP objectives.
For a more detailed summary, see the News and Views section of Nature Physics, October 2007 on the UNIGE website.
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Figure1: Scheme of the Entanglement Swapping setup |
Enhancement of the recombination rate of InAs quantum dots coupled to micro-cavities emitting at the telecom wavelengths
Applied Physics Letters 91, 123115 (2007)
L. Balet, M. Francardi, A. Gerardino, N. Chauvin, B. Alloing, C. Zinoni, C.
Monat, L. H. Li, N. Le Thomas, R. Houdré and A. Fiore.
Optics Letters 32, 2747
(2007)
N. Chauvin, L. Balet, B. Alloing, C. Zinoni, L. Li, A. Fiore, L. Grenouillet, P.
Gilet, N. Olivier, A. Tchelnokov, M. Terrier and J.-M. Gérard.
Quantum computing and quantum communication need sources of single
indistinguishable photons emitting at telecom wavelengths. Such requirements are
reachable using single quantum dots (QDs) embedded in micro-cavities. The
coupling of a QD with the cavity mode increases the recombination rate of the QD
exciton due to the Purcell effect. Thus the impact of the decoherence processes
is reduced and an increase of the repetition rate of the single photon source is
possible. Moreover the coupling of the QD emission with the mode enables good
collection efficiency.
Micro-photoluminescence (MPL) and time-resolved experiments have been performed
on InAs QDs embedded in photonic crystal (PhC) and micro-pillar (MP) cavities.
The QD growth and cavity fabrication have been optimized for emission at 1300
nm. The cavity modes present a high quality factor: up to 15000 for the PhC
cavities and up to 2500 for the MP cavities.
Studies performed on PhC cavities have revealed an increase in the intensity of
single QD lines when tuned with the cavity mode. Time resolved experiments
performed on these single QD lines have revealed an enhancement of the
recombination rate up to eightfold.
An increase of the recombination rate by a factor 2 is also observed for an
ensemble of QDs coupled to one mode of a MP cavity.
These results are very promising for the realization of efficient single photon
sources based on single QDs in a micro-cavity.
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Figure1: Time resolved dynamics of QDs spatially
outside the PhC region (blue squares) and of a single exiton line in
resonance of the cavity mode (black triangle) |
August 2007
Entanglement percolation in quantum networks
Nature Physics, 3, 256 (2007)
Antonio Acín, J. Ignacio Cirac and Maciej Lewenstein
Overview
The standard scenario in any quantum communication application consists of
several distant nodes that can exchange information encoded on quantum particles
through quantum channels, e.g. photons sent through optical fibers. The nodes
aim at establishing long-distance perfect quantum correlations, or maximally
entangled states, by performing local operations on each node and exchanging
classical communication. Therefore, in order to optimize the operation of a
quantum network, it is required to design efficient protocols for the
establishment of maximally entangled states between different distant nodes.
Until now, the standard solution for the distribution of entanglement between
distant nodes was by means of quantum repeaters. In this scenario, two distant
nodes are connected by a chain of quantum repeaters in a one-dimensional
configuration, see also Figure 1(a), below. General quantum networks, however,
have a richer and more connected structure, see also Figure 1(b) and 1(c). Our
recent work shows that intriguing quantum phenomena appear when studying the
distribution of entanglement through these more connected networks, depending on
the way the nodes are connected and the entanglement parameters characterizing
these connections. Actually, the distribution of entanglement through these
networks defines a new type of phase transition. This entanglement phase
transition is related to classical percolation, a concept that is well known in
Statistical Mechanics, so we named this phenomenon Entanglement Percolation.
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Figure1: Diagram illustrating the distinction
between a one-dimensional quantum network (a) and the richer structure
of a more general quantum network (b,c). |
July 2007
Twisted photons
Nature Physics, 3, 305 (2007)
G. Molina-Terriza, J. P. Torres and L. Torner
Overview
Quantum optical information applications make use of only a portion of the rich structure of atoms and photons. Most of these applications make use of the polarization or spin angular momentum of photons. This corresponds to using two-dimensional systems, that is systems whose state can be described by a combination of two orthogonal states, as any polarization state can be described by weighted superpositions of two linear or circular polarization states.
But the total angular momentum can also contain an orbital contribution, which comes from a more complex combination of the phase and amplitude profiles of an optical field. Contrary to the case of polarization, the orbital angular momentum lives in an infinite dimensional Hilbert space. Indeed, the dimensions of the working space can be readily tailored. This offers the possibility to explore quantum algorithms that either inherently live in a higher dimensional Hilbert space (qudits), or exhibit enhanced efficiency in increasingly higher dimensions.
In the May 2007 issue of Nature Physics (see Nature Physics 3, 305, 2007 and cover page) researchers Molina-Terriza, Torres and Torner, from ICFO-Institute of Photonic Sciences in Barcelona, review progress in the generation, understanding and use of the orbital angular momentum of photons. The orbital angular momentum of photons can be used to demonstrate the violation of bipartite, three dimensional Bell inequalities, to implement new protocols such as the so called quantum coin tossing, to generate quantum states in ultra-high dimensional spaces, to implement new quantum cryptography protocols, and as an powerful enabling tool to generate and to control multidimensional quantum states of matter, and therefore adds to the existing techniques for the full control of atoms.
The exploration of the orbital angular momentum of photons is an important tool of the Qubit Applications Project (QAP). It is related to the development of theory and design of experiments to exploit the rich structure of photons, which includes the development of techniques for the independent control of polarization and transverse wave-vector, and the investigation of new quantum communication protocols using the space degree of freedom of single photons.
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Figure: What is the shape of a photon which carries
orbital angular momentum? |
Trapped Ion Chain as a Neural Network: Error-Resistant Quantum Computation
Physical Review Letters, 98, 023003 (2007)
M. Pons, V. Ahufinger, C. Wunderlich, A. Sanpera, S. Braungardt, A. Sen(De), U. Sen, and M. Lewenstein
Overview
Exposing an ion - that is part of a linear array of ions confined in a Paul
trap - to a qubit-state-dependent force gives rise to a long-range interaction
between individual ionic qubits. In the January issue of Physical Review Letters
QAP researchers show that taking advantage of this long
range interaction an array of ions may be employed to realize a neural network
composed of individual atoms. This network permits storage of information
distributed over the whole atomic array. Moreover, error-resistant quantum
computation may be implemented using such a neural network.
As part of Subproject 4 of QAP the research group at the
University of Siegen
works on the implementation of ion spin molecules and will explore their
suitability, for instance, for realizing such a neural network.
June 2007
Remote preparation of an Atomic Quantum Memory
Physical Review Letters, 98, 050504 (2007)
Wenjamin Rosenfield, Stefan Berner, Jürgen Volz, Markus Weber, and Harald Weinfurter
Overview
Remote state preparation of a distant atomic quantum memory has been
demonstrated by researchers at Ludwig
Maximillians University (LMU), Germany. This is a significant step towards
the development of quantum repeaters, and quantum networks – two of the
principal research interests in the EU Project QAP.
Many of the fundamental concepts in quantum communication and quantum
information processing are predicated on the ability to faithfully map quantum
information between photons and matter-based quantum processors. Entanglement
between matter and light is crucial for this task. In this work, researchers at
LMU experimentally demonstrate the suitability of atom-photon entanglement as an
interface between a quantum memory device and a quantum communication channel.
In the demonstration at LMU, a single rubidium atom acting as the quantum memory
is prepared in a desired quantum state by a remote sender (Alice) using a remote
state preparation (RSP) protocol. The RSP protocol consists of three main steps.
Initially, entanglement is generated between the spin of a single Rubidium atom
confined in a dipole trap, and the polarization of a single spontaneously
emitted photon; the photon is then transferred to Alice via an optical fiber.
Secondly, Alice imprints the desired qubit on the photon using the spatial modes
of a polarization-independent Mach-Zehnder interferometer. Finally, the spatially
encoded qubit is transferred to the spin state of the atom by performing a
Bell-state measurement in the joint polarization - spatial-mode Hilbert space of
the photon. This is possible because of the atom-photon entanglement generated
in the first step.
The success of the RSP protocol described above has been verified at LMU by
conducting full quantum state tomography of the atomic qubit, after the
preparation process. The mean fidelity of quantum state transfer was found to be
82.2%. This work marks a significant step towards implementation of an atomic
quantum repeater.
Globally Controlled Quantum Wires for Perfect Qubit Transport, Mirroring, and Computing
Physical Review Letters, 97, 090502 (2006)
Joe Fitzsimmons and Jason Twamley
Overview
Recent work by researchers at Oxford and Macquarie Universities has shown
that the necessary requirements for practical quantum computing may be lower
than previously thought. In their paper, Joe Fitzsimons and Jason Twamley
outline a scheme for performing universal quantum computation within a uniform
Ising spin chain without the need to control individual spins separately.
The need to individually address qubits within a quantum computer has proved a
roadblock to achieving scalable quantum computing within many systems. While a
number of architectures exist which overcome this problem using periodic
arrangements of different types, or species, of qubits, this new scheme
substantially lowers the experimental requirements, requiring only a single
physical species of qubit together with a common physical interaction.
The paper includes a prescription for quantum state transfer, the task of moving
quantum information from one location to another, as well as a procedure for
efficiently mirroring the order of qubits stored within the spin chain. These
are both important tasks within quantum communication, and it is likely that
similar quantum wires will provide important communications buses within any
large scale solid-state quantum processor.
Additionally, the paper describes how universal computing can be achieved within
the spin chain without resorting to local control. The density with which
logical qubits can be packed (½) within the chain is the highest yet achieved
within such a scheme, and has since been increased to the maximum possible
density of one qubit per spin (quant-ph/0606188),
offering computational power competitive with locally controlled schemes.
Shortly after publication of this paper, a successful experimental
implementation of the scheme was reported using NMR techniques (quant-ph/0606188).
This work substantially lowers the barriers to scalable solid-state quantum
computing.
May 2007
Observation of Entanglement of a Single Photon with a Trapped Atom
Physical Review Letters, 96, 030404 (2006)
J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Saucke, C. Kurtsiefer, and H. Weinfurter
Overview
Entanglement between the polarization of a single photon and the internal
state of a single neutral atom has been observed by researchers at Ludwig
Maximillians University (LMU), Germany. This is a crucial step towards
implementation of long range quantum networks: one of the principal areas of
research in the EU Integrated Project QAP .
Entanglement is a key element for quantum communication and information
applications. Future applications such as quantum networks and the quantum
repeater are predicated on the distrubution of entanglement between separate
quantum processors. For this purpose, entanglement between different quantum
objects such as atoms and photons forms the interface between atomic quantum
processors and photonic quantum communication channels, finally allowing the
distibution of quantum information over arbitrary distances.
In this implementation a single Rubidium atom, confined within a dipole trap of
radius 3.5µm, acts as a quantum processor. The atom is trapped using a far
off-resonance laser field. The instantaneous dipole moment induced on the atom
by the field results in an intensity dependent force upon the atom. For a large
negative frequency detuning this dipole force pushes atoms towards regions of
higher laser intensity, thus allowing confinement of atoms within a region of
suitably intersecting laser beams.
Selective pumping prepares the trapped atom in an excited hyperfine state which
can decay to three possible ground states with magnetic quantum numbers MF=-1,0
or +1 by spontaneously emitting a σ+, π or σ- polarized photon, respectively.
Photons with σ-polarization are detected in the same spatial mode and analysed
to determine their polarization while those with π-polarization are ignored.
Provided the emission processes are indistinguishable in all degrees of freedom
other than polarization, the atom-photon system is in a maximally entangled
state. This entanglement has been verified at LMU using a full tomographic
analysis of the atomic state via a state selective stimulated Raman adiabatic
passage (STIRAP) technique.
The techniques employed at LMU represent an important step towards an interface
between a quantum computer and a photonic quantum communication channel.



















With QLib, you can simply generate a few million random density matrices and
check. In the graph to the right you see 2d projections of the “hypersphere”.















