Principal Investigator: Professor Martin PlenioThe ProjectQuantum Networks: Qudit and continuous variable networks The goal of this workpackage is to develop theory and design of experiments exploiting the rich structure of photons to build error correction and avoidance schemes, and to implement few-qubit algorithms. All computational devices – classical and quantum – are subject to unwanted interactions with their environment which will lead to operational errors. In classical applications many errors may be suppressed by ensuring the logical bits are robust against background environmental noise. In addition, classical bits may be processed in a redundant fashion – essentially using copies to protect against errors. Such protections are not applicable in quantum applications due to the physical nature of qubit encoded systems: the no-cloning theorem forbids the copying of qubits and thus negates the classical scheme of redundant calculation. Quantum error correction aims at protecting the coherence of quantum states against noise. The general principle is to encode a single logical qubit on to several physical qubits to make the states robust against the effects of noise. |
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This project will investigate how the individual degrees of freedom (polarization, transverse wavevector, time-bin modes, etc.) may be manipulated coherently, both separately and collectively, for use in error correction. New quantum communication protocols using space and time degrees of freedom of a single photon together with its polarization for realising the quantum channel coding theorem will be assessed and investigated. Joint quantum operations, such as the CNOT gate and controlled phase gates, between more than one photonic degree of freedom will be designed and implemented.
A fibre-optic architecture is adopted within the QAP Quantum Network project. Realistic models of decoherence within optical fibres will be considered within this workpackage. Mechanisms of noise reduction will be designed, based upon phase shifters. Gaussian quantum channels are a natural model for optical links such as fibres. Their capacity (maximum achievable information rate) and the possibility of enhancing it with entangled continuous-variable states will be investigated.
Quantum Networks: Multi-particle and qudit entanglement purification and algorithms
The aim of this workpackage is to design experiments and develop theory for realizing entanglement distribution over networks in the form of multi-partite and multimode states.
Photons have several degrees of freedom (polarization, transverse wavevector, time-bin modes, etc.) with the potential for quantum information encoding. The large information capacity of photonic qudit states (d-level quantum systems) will be applied to quantum communication networks, by exploring the possibility of using them in teleportation schemes and other protocols. In particular, protocols with no qubit based solutions will be investigated. Protocols designed in this workpackage will be implemented using quantum gates developed in the “Qudit and continuous variable networks” project (above).
Entanglement distribution is a key goal of quantum networks, with practical use in telecommunications infrastructures for example. Unwanted decoherence effects during transmission of light over a network will inevitably corrupt information encoded states. Purification and concentration schemes will be necessary to enhance entanglement to practically useful levels. Procrustean protocols for entanglement generation using high-brightness sources with quantum-correlated photon numbers and number resolving detectors will be implemented in this workpackage. Continuous variable encoding of the optical field will be used, with state conditioning via measurement. The feasibility of protocols for entanglement enhancement at remote locations using realistic sources, detectors and linear optics will be investigated. Concatenation of two stages of conditioning is a long term goal for demonstration of the power of iteration. Furthermore, quantum relay protocols will be investigated experimentally for entanglement distribution over large distances.
Error detection and error correction on single photons is of particular use in quantum communication techniques employing the polarization and field mode. Optimal schemes for protecting the polarization degree of freedom by entangling it with other degrees of freedom will be established in theoretical work. Experimental production of qu-quads (4-dimensional systems) will lead to production of entangled qubits of high quality by error filtration. Partners at the Universite Libre de Bruxelles (ULB) and the Centre for Mathematics and Computer Science (CWI) have shown that higher dimensional entangled systems may be able to close the detection loophole in non-locality tests. Partner ULB will develop the qu-quad experiment for non-locality tests on entangled 4-dimensional systems.
Quantum communication may be used to toss coins more random than is possible in classical protocols. Recent experiments have focused on bit string generation that is easier to implement experimentally than tossing a single coin. This workpackage will attempt to realize an experiment in which a single coin is tossed in such a way that no party can bias the coin maximally (this is impossible classically)
Entanglement Generation/Propagation, Phase Transitions and Adiabatic Quantum Algorithms in Interacting Quantum Systems
Entanglement is a quantity that may play a crucial role in the description and understanding of critical phenomena occurring in quantum many-body systems. Quantum correlations are behind the strong fluctuations many-body systems exhibit near critical points. Their study is thus expected to bring a new insight into critical phenomena. We aim to understand the static and dynamic entanglement properties of quantum many body systems with the focus on those models that are physically realizable and relevant to schemes such as adiabatic quantum computation. Furthermore, we want to develop novel ways to create and distribute entanglement without the use of detailed spatial and temporal control.
Researchers based at Imperial College will study quantum many-body systems with the aim of maximising entanglement generation without detailed local control. Techniques from optimisation theory previously applied to the study of quantum entanglement will be utilised to achieve this goal. System-independent considerations from this work will be placed in the context of experimental realisations developed in other QAP work packages. In particular, interesting demonstrator experiments will be designed for ion trap and distributed quantum dot arrangements.
Entanglement behaviour at critical points will be studied by solving models of many-body systems. Starting with two-partite systems the goal is to calculate entanglement for any set of particles. This work will be carried out by researchers at the Slovak Academy of Sciences (Partner IPSAS). Subsequently, possible links between the theory of phase transitions and multi-partite entanglement behaviour at critical points will be investigated by collaborators at IPSAS and Imperial College. The tools developed here may help to detect critical points by analyzing the entanglement properties of a quantum system.
Ideas coming from quantum information may produce real progress in well-established branches of physics like Renormalization Group Theory. Partners based at the University of Barcelona will investigate the relation between irreversibility of renormalization group trajectories and coarse graining strategies on quantum states. In addition, different representations of entanglement in translation invariant spin networks will be investigated for efficient numerical simulation. These techniques will be applied to time evolution simulations of large quantum systems in connection with adiabatic quantum computation.
Other QAP Activities
Researchers at Imperial College, London are also involved in other QAP projects:
- Testing small-scale quantum networks and devices with HPLB
- Optimal control of quantum systems with finite degrees of freedom: spins and beyond with TU-Munich
- Hamiltonian simulation and decoherence-free subspaces with TU-Munich
- Algorithms and complexity with Tel-Aviv U
- Algorithmic methods with UPS
- Protocols for quantum commerce with CWI
- Toolbox for quantum multi-user protocols with ICFO
- Architectures with UMK
- Testing quantum systems with IPSAS
List of Publications
QAP
K. M. R. Audenaert and M. B. Plenio, When are correlations quantum? - Verification and quantification of entanglement by simple measurements., New J. Phys 8 266 (2006) quant-ph/0608067
S. Anders, M. B. Plenio, W. Dür et al, Ground state approximation for strongly interacting systems in arbitrary dimension, Phys. Rev. Lett. 97 107206 (2006) quant-ph/0602230
A. Feito, QUANTAVO: Manual and Examples of a software package for the analysis of continuous variable networks (2006)
M. Cramer, J. Eisert and M. B. Plenio, Statistics dependence of the entanglement entropy (2006) quant-ph/0611264
O. Dahlsten and M. B. Plenio, Exact entanglement probability distribution of bi-partite randomised stabilizer states, Quant. Inf. Comp 6 527 (2006) quant-ph/0511119
J. Eisert, Optimizing over several sites in DMRG to find quantum ground states is NP-hard, accepted for publication in Phys. Rev. Lett. quant-ph/0609051
J. Eisert, F. Brandao, and K. Audenaert, Quantitative entanglement witnesses (2006) quant-ph/0607167
J. Eisert, T. J. Osborne, General entanglement scaling laws from time evolution, Phys. Rev. Lett. 97 150404 (2006) quant-ph/0603114
J. Eisert, M. B. Plenio, D. E. Browne, S. Scheel, A. Feito, On the experimental feasibility of continuous-variable optical entanglement distillation (2006) quant-ph/0604163
D. Gross, K. Audenaert, J. Eisert, Evenly distributed unitaries: on the structure of unitary designs (2006) quant-ph/0611002
D. Gross, J. Eisert, Computational potency of quantum many-body systems (2006) quant-ph/0609149
O. Guehne, P. Hyllus, O. Gittsovich et al, Covariance matrices and the separability problem (2006) quant-ph/0611282
D. Gross, K. Kieling and J. Eisert, Potential and limits to cluster state quantum computing using probabilistic gates, Phys. Rev. A 74 042343 (2006) quant-ph/0605014
D. Gross, T. Rudolph, J. Eisert, Percolation, renormalization, and quantum computing with non-deterministic gates (2006) quant-ph/0611140
M. J. Hartmann, F. G. S. L. Brandao and M. B. Plenio, Strongly Interacting Polaritons in Coupled Arrays of Cavities, Nature Physics 2 849 (2006) quant-ph/0606097
M. Hein, W. Dür, J. Eisert et al, Entanglement in Graph States and its Applications (2006) quant-ph/0602096
S. F. Huelga and M. B. Plenio, When cooler is not better: Stochastic Resonance Phenomena in Quantum Many-Body Systems (2006) quant-ph/0608164
M. J. Hartmann, M. E. Reuter and M. B. Plenio, Excitation and Entanglement Transfer Near Quantum Critical Points, New J Phys 8 94 (2006) quant-ph/0511185
M. Lucamarini, D. Vitali and P. Tombesi, Quantum-limited force measurement with an optomechanical device (2006) quant-ph/0610236
R. Oliveira, O. C. O. Dahlsten and M. B. Plenio, Efficient Generation of Generic Entanglement (2006) quant-ph/0605126
R. Orus, J. I. Latorre, J. Eisert et al, Half the entanglement in critical systems is distillable from a single specimen, Phys. Rev. A 73 060303(R) (2006) quant-ph/0509023
M. B. Plenio and S. Virmani, An Introduction to entanglement measures, Quant. Inf. Comp 7 1 (2007) quant-ph/0504163
M. Paternostro, D. Vitali, S. Gigan et al, Creating and probing macroscoping entanglement with light, submitted to Phys. Rev. Lett. quant-ph/0609210
A. Retzker and M. B. Plenio, Fast cooling of trapped ions using the dynamical Stark shift gate (2006) quant-ph/0607199
C. Schön, K. Hammerer, M. M. Wolf, J. I. Cirac, and E. Solano, Sequential Generation of Matrix-Product States in Cavity QED, submitted to Phys. Rev. A quant-ph/0612101
S. Scheel, W. J. Munro, J. Eisert, K. Nemoto, P. Kok, Feed-forward and its role in conditional linear optical quantum dynamics, Phys. Rev. A 73 034301 (2006) quant-ph/0509075
K. M. R. Audenaert, A Sharp Fannes-type Inequality for the von Neumann Entropy (2006) quant-ph/0610146
F. G. S. L. Brandao, M. Horodecki, M. B. Plenio and S. Virmani, Remarks on the equivalence of full additivity and monotonicity for the entanglement cost, submitted to OSID quant-ph/0702136
F. G. S. L. Brando, M. Hartmann and M. B. Plenio, Dynamical Stark-shift induced simplification of non-linearities, submitted to Phys. Rev. Lett. quant-ph/07052398
M. Cramer, C. M. Dawson, J. Eisert, T. J. Osborne, Quenching, relaxation, and a central limit theorem for quantum lattice systems, submitted to Phys. Rev. Lett. cond-mat/0703314
O. Dahlsten, R. Olivera and M. B. Plenio, Emergence of typical entanglement in two-party random processes, submitted to J. Phys. A quant-ph/0701125
J. Eisert, T. Tyc, T. Rudolph, B. C. Sanders, Gaussian quantum marginal problem, submitted to Commun. Math. Phys. quant-ph/0703225
D. Gross, Hudson's Theorem for finite-dimensional quantum systems, J. Math. Phys. 47 122107 (2006) quant-ph/0602001
D. Gross, Non-negative Wigner functions in prime dimensions, Appl. Phys. B 86 367 (2007) quant-ph/0702004
D. Gross, J. Eisert, Novel schemes for measurement-based quantum computation, Phys. Rev. Lett. 98 220503 (2007) quant-ph/0609149
M. Hartmann, F. G. S. L. Brando, and M. B. Plenio, Effective spin models in coupled arrays of micro-cavities, submitted to Phys. Rev. Lett. quant-ph/07043056
M. Hayashi, D. Markham, M. Murao, M. Owari, S. Virmani, Bounds on Multipartite Entangled Orthogonal State Discrimination Using Local Operations and Classical Communication, Phys. Rev. Lett. 96 040501 (2006) quant-ph/0506170
M. Hartmann and M. B. Plenio, Effective spin models in coupled arrays of micro-cavities, submitted to Phys. Rev. Lett. quant-ph/07042575
M. Hartmann, M. E. Reuter and M. B. Plenio, Excitation and Entanglement Transfer Near Quantum Critical Points, Opt. Spect. 103 22 (2007) quant-ph/0608051
K. Kieling, D. Gross, J. Eisert, Cluster state preparation using gates operating at arbitrary success probabilities, accepted for publication in New J. Phys. quant-ph/0703045
I. Katz, A. Retzker, R. Straub, R. Lifshitz, Classical to Quantum Transition of a Driven Nonlinear Nanomechanical Resonator (2007) quant-ph/0702255
N. M. VanMeter, P. Lougovski, D. B. Uskov, K. Kieling, J. Eisert, J. P. Dowling, A General Linear-Optical Quantum State Generator, submitted to Phys. Rev. Lett. quant-ph/0612154
D. Markham, A. Miyake, S. Virmani, Entanglement and local information access for graph states, accepted for publication in New J. Phys. quant-ph/0609102
M. B. Plenio, Remarks on duality transformations and generalized stabilizer states, accepted for publication in J. Mod. Opt. quant-ph/0703007
M. B. Plenio and S. Virmani, Spin chains and channels with memory, submitted to Phys. Rev. Lett. quant-ph/0702059
M. Reuter, M. Hartmann and M. B. Plenio, Geometric phases and critical phenomena in a chain of interacting spins, Proc Roy Soc Lond A 463 1271 (2007) quant-ph/0612194
A. Serafini, O. Dahlsten, D. Gross and M. B. Plenio, Canonical and micro-canonical typical entanglement of continuous variable systems, submitted to J. Phys. A quant-ph/0701051
A. Serafini, O. C. O. Dahlsten and M. B. Plenio, Thermodynamical state space measure and typical entanglement of pure Gaussian states, Phys. Rev. Lett. 98 170501 (2007) quant-ph/0610090
D. Tsomokos, S. F. Huelga , M. Hartmann, and M. B. Plenio, Dynamics of chains of superconducting devices, New J. Phys. 9 79 (2007) quant-ph/06011077
K. M. R. Audenaert, M. Nussbaum, A. Szkola et al, Asymptotic Error Rates in Quantum Hypothesis Testing (2007) arXiv:0708.4282
G. McConnell and D. Gross, Efficient 2-designs from bases exist (2007) quant-ph/0710.1502
M. Cramer, S. Ospelkaus, C. Ospelkaus et al, Do mixtures of bosonic and fermionic atoms adiabatically heat up in optical lattices?, submitted to Phys. Rev. Lett.
C. M. Dawson, J. Eisert and T. J. Osborne, Unifying variational methods for simulating quantum many-body systems, submitted to Phys. Rev. Lett. quant-ph/07053456
F. G. S. L. Brandao and J. Eisert, Correlated entanglement distillation and the structure of the set of undistillable states, submitted to J. Math. Phys.
D. Gross and J. Eisert, Quantum Margulis expanders, submitted to Quant. Inf. Comp
D. Gross, J. Eisert, N. Schuch et al, Measurement-based quantum computation beyond the one-way model, Phys. Rev. A 76 052315 (2007)
C. Genes, D. Vitali, P. Tombesi et al, Ground-state cooling of a micromechanical oscillator: generalized framework for cold damping and cavity-assisted cooling schemes (2007)
M. J. Hartmann, F. G. S. L. Brandao and M. B. Plenio, A two-component Bose-Hubbard model in coupled micro-cavities, submitted to Phys. Rev. Lett. arXiv:0706.2251
M. J. Hartmann and M. B. Plenio, Migration of bosonic particles across a Mott insulator to superfluid phase interface, submitted to Phys. Rev. Lett.
K. Kieling, J. Eisert, Percolation in quantum computation and communication, Springer (2007) arXiv:0712.1836
R. Prevedel, A. Stefanov, Ph. Walther et al, Experimental realization of a quantum game on a one-way quantum computer, New J. Phys. 9 205 (2007) arXiv:0708.1129
M. B. Plenio and S. Virmani, Critical phenomena and the capacity of quantum channels with memory, submitted to New J. Phys. arXiv:0710.3299
R. Hübner, C. Kruszynska, S. Anders et al, Renormalization algorithm with graph enhancement (2008)
A. Retzker, J. I. Cirac, M. B. Plenio, B. Reznik, Detection of acceleration radiation in a Bose-Einstein condensate, submitted to Phys. Rev. Lett. quant-ph/0709.2425
M. Stütz, S. Gröblacher, Th. Jennewein et al, How to create and detect N-dimensional entangled photons with an active phase hologram, App. Phys. Lett. 90 261114 (2007)
A. Serafini, A. Retzker and M. B. Plenio, Towards linear phononics and nonlocality tests in ion traps, submitted to Phys. Rev. Lett. quant-ph/0708.0851
D. Vitali, G. Di Guiseppe, D. Sajeev et al, Dynamical decoupling schemes for inhibiting decoherence in the propagation of single-photon polarization qubits, Proceedings PhysCon2007 (2007)
F. G. S. L. Brandao and J. Eisert, Correlated entanglement distillation and the structure of the set of undistillable states, J. Math. Phys. 49 042102 (2008) arXiv:0709.3835
F. G. S. L. Brandao and M. B. Plenio, A reversible theory of entanglement and its relation to the second law (2007) arxiv:0710.5827
M. Cramer, C. M. Dawson, J. Eisert et al, Exact Relaxation in a Class of Nonequilibrium Quantum Lattice Systems, Phys. Rev. Lett. 100 030602 (2008) cond-mat/0703314
F. Caruso, J. Eisert, V. Giovannetti et al, Multi-mode bosonic Gaussian channels, submitted to New J. Phys. arXiv:0804.0511
M. Cramer, A. Flesch, I. P. McCulloch et al, Exploring local quantum many-body relaxation by atoms in optical superlattices, accepted for publication in Phys. Rev. Lett. arXiv:0805.0798
M. Cramer, A. Sefafini and J. Eisert, Locality of dynamics in general harmonic quantum systems, Scuola Normale Pisa (2008) quant-ph/0803.0890
A. Feito, Quantavo: a Maple Toolbox for Linear Quantum Optics (2008) arxiv:0806.2171
O. Gittsovich, O. Guehne, P. Hyllus et al, Unifying several separability conditions using the covariance matrix criterion, submitted to Phys. Rev. A quant-ph/0803.0757
R. Huebener, C. Kruszynska, L. Hartmann et al, Renormalization algorithm with graph enhancement, submitted to Phys. Rev. Lett. arxiv:0802.1211
M. J. Hartmann and M. B. Plenio, Steady state entanglement in the mechanical vibrations of two dielectric membranes, submitted to Phys. Rev. Lett. arxiv:0806.1616
I. E. Linington, P. A. Ivanov, N. V. Vitanov et al, Robust control of quantized motional states of a chain of trapped ions by collective adiabatic passage, accepted for publication in Phys. Rev. A arxiv:0801.1588
M. Navascues, S. Pironio, and A. Acín, A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations, accepted for publication in New J. Phys. arXiv:0803.4290
A. Retzker, R. Thompson, D. Segal et al, Double wells, scalar fields and quantum phase transitions in ions traps, submitted to arxiv arxiv:0801.0623
M. M. Wolf, J. Eisert, T. S. Cubitt et al, Quantum evolution from a snapshot, submitted to Phys. Rev. Lett. quant-ph/0711.3172
Related work
M. Cramer, J. Eisert, M. B. Plenio, J. Dreissig, An entanglement-area law for general bosonic harmonic lattice systems, Phys. Rev. A 73 012309 (2006) quant-ph/0505092
J. Eisert, D. Gross, Multi-particle entanglement, Lecture notes in quantum information (2006) quant-ph/0505149
J. Eisert, M. M. Wolf, Gaussian quantum channels, Continuous variable quantum information processing (Imperial College Press, London, 2006) (2006) quant-ph/0505151
D. Vitali, S. Gigan, A. Ferreira et al, Optomechanical entanglement between a movable mirror and a cavity field (2006) quant-ph/0609197
M. Cramer and J. Eisert, Correlations, spectral gap, and entanglement in harmonic quantum systems on generic lattices, New J. Phys 8, 71 (2006) quant-ph/0509167
J. Eisert, M. M. Wolf, Quantum computing, Handbook of innovative computational paradigms (Springer, New York, 2006) (2006) quant-ph/0401019
P. Hyllus, J. Eisert, Optimal entanglement witnesses for continuous-variable systems, New J. Phys. 8, 51 (2006) quant-ph/0510077
K. Kieling, D. Gross, J. Eisert, Optimal strategies for fusing optical cluster states (2006) quant-ph/0601190
K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. OBrien, and A. G. White, Time-Reversal and Super-Resolving Phase Measurements, Phys. Rev. Lett. 98 223601 (2007) quant-ph/0511214