Principal Investigators: Professor Vladimir Buzek / Dr Eva Majkova
The Project
The activities of Research Center for Quantum Information are
predominantly in the QAP subprojects Theory, Quantum simulations and Quantum
memory.
Testing quantum devices
The main purpose for the development of testing methods is to provide
experimentalists with tools that enables them to verify theoretical
proposals. The importance of this research is clearly seen from the fact
that the subject stands directly between theory and experiment. The
estimation of quantum states and quantum processes is a complex task,
because the number of parameters increases exponentially with the size of
the system (quantified in number of qubits). Our goal is to analyze
incomplete estimation methods, develop new process estimation schemes and
study various simpler estimation tasks such as quantum discrimination and
identification problems [1-4,8].
We have used the maximum likelihood method (ML) for a derivation of physical
approximations of truly unphysical operations. In particular, we analyze the
physical approximations of the Universal-NOT gate, the quantum nonlinear
polarization rotation and a “square” map. Having the result of ML, we
examined retrospectively the quality of the experiment. Depending on the
resulting value of the ML functional we can determine (physical) consistency
of the input data. We have compared the results with analytical approaches,
in which the optimality is defined with respect to different "distance"
functions. We have found that for U-NOT operation and quantum nonlinear
polarization the analytical solutions do agree with the ML results. For the
square transformation the results are different. However, our conclusion is
that ML method provides us with the correct concept of best physical
approximation, because it is based on the operational procedure. In
particular, on the ML method that translates the experimental results into
theoretical description. In this sense the approach is very physical.
We also addressed the role of initial correlations in quantum process
tomography. Behind this idea is the observation that direct tomography
methods (not using statistical estimation tools like maximum likelihood)
typically result in nonphysical maps, i.e. transformations that are not
completely positive. We proposed an artificial model in which any
transformation obtained in process tomography can be considered as physical.
Finally, we proposed two more realistic models within which the complete
positivity is not guaranteed, i.e. the corresponding quantum processes does
not have to be completely positive. Within these models we describe the
implementation of the U-NOT operation, which is in some sense the most
unphysical linear operation on the single qubit.
Quantum protocols
The privacy [9-11] of communicating participants is often of paramount
importance, but in some situations it is an essential condition. A typical
example is a fair (secret) voting. We analyze in detail communication
privacy based on quantum resources, and we propose new quantum protocols
leading to quantum-based voting scheme. Apart of this we were also analyze
the optimality of private quantum channels, i.e. a secure transmissions of
quantum information by using a shared classical key.
Quantum algorithms
We investigated quantum walks [5] in multiple dimensions with different
quantum coins. We augmented the model by assuming that at each step the
amplitudes of the coin state are multiplied by random phases. This model
enables us to study in detail the role of decoherence in quantum walks and
to investigate the quantum-to-classical transition. We also provided
classical analog of the quantum random walks studied. Interestingly enough,
it turned out that the classical counterparts of some quantum random walks
are classical random walks with a memory and biased coin. In addition random
phase shifts "simplify" the dynamics (the cross-interference terms of
different paths vanish on average) and enabled us to give a compact formula
for the dispersion of such walks. We proposed a quantum walk implementation
of Parrondo's game and compared with classical implementation.
Quantum entanglement
We analyzed the behavior of entanglement under local actions [6,12]. It was
shown that entanglement induced ordering (for arbitrary measure) is not
preserved under local operations performed on one system only. We addressed
the problem of the generation of entanglement. Using tools of quantum
information theory we study the ground state of the radiation-matter
interaction Hamiltonian [13,14], in the long wavelength limit, in three
different scenarios: (a) Dicke Hamiltonian, (b) Dicke Hamiltonian plus
counter-rotating terms, (c) Dicke Hamiltonian plus counter rotating terms
and quadratic term. We show that, in all three cases, the interaction
between a system of distinct two-level systems and one mode of radiation
field leads to the quantum correlation between individual two-level systems,
and to the correlation between the whole two-level system and the radiation
field as well. In the case (a) the ground state of the Hamiltonian exhibits
quantum-phase-like transitions for the concurrence between atoms.
OTHER QAP activities
- testing quantum decoherences with MACQ
- testing quantum entanglement with IMPERIAL
- comparison of quantum memories with UG
List of Publications
QAP
[1] Mário Ziman : Quantum process tomography: the role of initial correlations, quant-ph/0603166
[2] Martin Plesch, Mário Ziman, Vladimír Bužek, Peter Štelmachovič: Estimation of potentially unphysical maps, Open Systems and Information Dynamics 13, 255-262 (2006)
[3] Mário Ziman : Notes on optimality of direct characterisation of quantum dynamics LANL preprint archive quant-ph/0603151
[4] Janos A. Bergou, Vladimír Bužek, Edgar Feldman, Ulrike Herzog, Mark Hillery : Programmable quantum state discriminators with simple programs, Phys.Rev.A 73, 062334 (2006), quant-ph/0602164
[5] Jozef Košík, Vladimír Bužek, Mark Hillery : Quantum walks with random phase shifts , Phys. Rev. A 74, 022310 (2006), quant-ph/0607092
[6] Derek McHugh, Mário Ziman, Vladimír Bužek : Entanglement, purity and energy: Two qubits vs Two modes, Phys.Rev.A 74, 0423903 (2006) quant-ph/0607012
[7] Mark Hillery, Mário Ziman, Vladimír Bužek : Approximate programmable quantum processors, Phys. Rev. A 73, 022345 (2006), quant-ph/0510161
V. Buzek, M. Hillery, M. Ziman, and M. Rosko, Programmable quantum processors, Quantum Information Processing 5 313-420 (2006)
M. Bonanome, M. Hillery, and V. Buzek, Applications of quantum algorithms to the study of group automorphisms, Phys. Rev. A 76 012324 (2007)
V. Buzek, M. Hillery and M. Ziman, Towards Quantum-based Election Scheme, Quantum Communication and Security (edited by M.Zukowski et al.) NATO Science for Peace and Security Series, D: Information and Communication Security 11 215--223 (2007)
J. Kosik, J. A. Miszczak and V. Buzek, Quantum Parrondo's game with random strategies, accepted for publication in J. Mod. Opt. arXiv:0704.2937
P. Rapcan, J. Calsamiglia, R. Munoz-Tapia, at al., Recycling of quantum information: Multiple observations of quantum systems, submitted to Phys. Rev. Lett. arXiv:0708.1086
M. Sedlak, M. Ziman, O. Pribyla, et al., Unambiguous coherent state identification: Searching a quantum database, Phys. Rev. A 76 022326 (2007) arXiv:0706.1892
M. Ziman, Incomplete quantum process tomography and principle of maximal entropy, submitted to Phys. Rev. A
M. Ziman and V. Buzek, Entanglement measures: State ordering vs local operations, Quantum Communication and Security (edit 196--204 (2007) arXiv:0707.4401
M. Ziman and V. Buzek, Universality and optimality of programmable quantum processors, Acta Phys. Hung. B 26 277-291 (2006) quant-ph/0612218
T. Heinosaari, P. Stano and D. Reitzner, Approximate Joint Measurability of Spin Along Two Directions, submitted to Eur. Phys. J. D arXiv:0801.2712
M. Koniorczyk, A. Varga, P. Rapcan et al, Quantum homogenization and state randomization in semi-quantal spin systems., Phys. Rev. A 77 052106 (2008) arXiv:0712.2136
D. Reitzner, M. Hillery, E. Feldman et al, Quantum Searches on Highly Symmetric Graphs, submitted to Phys. Rev. A arXiv:0805.1237
M. Sedlak and M. Plesch, Towards optimization of quantum circuits., Cent.Eur.J. Phys. 6 128-134 (2008) quant-ph/0607123
P. Stano, D. Reitzner and T. Heinosaari, Coexistence of qubit effects, accepted for publication in Phys. Rev. A arXiv:0802.4248
M. Sedlak, M. Ziman, V. Buzek et al, Unambiguous comparison of ensembles of quantum states., Phys. Rev. A 77 042304 (2008) arXiv:0712.1616
M. Ziman, Process positive-operator-valued measure: A mathematical framework for the description of process tomography experiments, accepted for publication in Phys. Rev. A arXiv:0802.3862
M. Ziman and T. Heinosaari, Discrimination of quantum observables using limited resources, Phys. Rev. A 77 042321 (2008) arXiv:0712.3675
Related work
[8] Mário Ziman, Martin Plesch and Vladimír Bužek : Reconstruction of superoperators from incomplete data, Foundations of Physics 36, 127-156 (2006), quant-ph/0406088
[9] Jan Bouda, Mário Ziman: Optimality of quantum private channels J. Phys. A: Math. Theor. 40 (2007) 5415-5426
[10] Mark Hillery, Mário Ziman, Vladimír Bužek, Martina Bielikova : Towards quantum-based privacy and voting, Physics Letters A 349, Issues 1-4 , pp 75-81 (2006), quant-ph/0505041
[11] Jan Bouda and Mário Ziman : Limits and restrictions of private quantum channel, quant-ph/0506107
[12] Mário Ziman and Vladimír Bužek : Entanglement-induced state ordering under local operations, Phys. Rev. A 73, 012312 (2006), LANL preprint archive quant-ph/0510017
[13] Vladimír Bužek, Miguel Orszag, and Marian Roško : Bužek, Orszag, and Roško Reply: Phys.Rev.Lett. 96, 089302 (2006)
[14] Vladimír Bužek, Miguel Orszag, Marian Roško : Instability and entanglement of the ground state of the Dicke model, Phys.Rev.Lett. 94, 163601 (2005), LANL preprint archive quant-ph/0503195
[15] Mário Ziman, Vladimír Bužek : Universality and optimality of programmable quantum processors, Acta Phys.Hung.B 26, 277-291 (2006)
[16] V.Bužek, M.Hillery, M.Ziman, and M.Roško : Programmable quantum processors, Quantum Information Processing 5, Num.5, pp.313-420 (2006)
P. Stano and J. Fabian, Control of electron spin and orbital resonance in quantum dots through spin-orbit interactions, Phys.Rev.B 77 045310 (2008) cond-mat/0611228
PRESS & MEDIA (in Slovak)
1.
interview with Prof. Bužek (9.2.2006, newspapers Sme)
2.
interview with Mario Ziman (popular science journal Quark/March)
3.
interview with Prof. Bužek (24.3.2007, newspapers Pravda)
4.
Newspaper article by Prof. Bužek in journal Týždeň (2007/08)