najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2019-10-4-398-401najo-511Research ArticlePHYSICSФИЗИКАAnalysis of the unambiguous state discrimination with unequal a priori probabilitiesGaidashA. A.

Kronverkskiy, 49, St. Petersburg, 197101

andrewdgk@gmail.comMedvedevaS. S.

Kronverkskiy, 49, St. Petersburg, 197101

mdvdv.svt@gmail.comMiroshnichenkoG. P.

Kronverkskiy, 49, St. Petersburg, 197101

ITMO UniversityRussian Federation201905082025104398–401Copyright © Gaidash A.A., Medvedeva S.S., Miroshnichenko G.P., 20252025Gaidash A.A., Medvedeva S.S., Miroshnichenko G.P.Gaidash A.A., Medvedeva S.S., Miroshnichenko G.P.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/511

In this paper, we study unambiguous state discrimination regarding advanced attack on phase-coded quantum key distribution protocol. We propose the method of optimal unambiguous state discrimination probability derivation as a function of a priori probabilities for signal states. The expression obtained as an example in case of two signal states explicitly demonstrates the additional term dependent on small deviations from equal a priori probabilities that may take place in real quantum key distribution implementations. Precise estimation of optimal unambiguous state discrimination probability is significant for complete evaluation of quantum key distribution security.

quantum key distributionunambiguous state discriminationThis work was financially supported by the Ministry of Education and Science of Russian Federation (contract No. 03.G25.31.0229).ReferencesBennett C.H., Brassard G. Quantum Cryptography: Public Key Distribution and Coin Tossing. Proceedings of ”International Conference on Computers, Systems and Signal Processing”, Bangalore, India, 09.12.1984, P. 17.Bennett C.H., Brassard G. Quantum Cryptography: Public Key Distribution and Coin Tossing. Proceedings of ”International Conference on Computers, Systems and Signal Processing”, Bangalore, India, 09.12.1984, P. 17.Ekert A. Quantum cryptography based on Bell’s theorem. Physical review letters, 1991, 67 (6), P. 661–663.Ekert A. Quantum cryptography based on Bell’s theorem. Physical review letters, 1991, 67 (6), P. 661–663.Vazirani U., Vidick T. Fully device independent quantum key distribution. Communications of the ACM, 2019, 62 (4), P. 133–133.Vazirani U., Vidick T. Fully device independent quantum key distribution. Communications of the ACM, 2019, 62 (4), P. 133–133.Minder M., Pittaluga M., et al. Experimental quantum key distribution beyond the repeaterless secret key capacity. Nature Photonics, 2019, 13, P. 334–338.Minder M., Pittaluga M., et al. Experimental quantum key distribution beyond the repeaterless secret key capacity. Nature Photonics, 2019, 13, P. 334–338.Razavi M., Leverrier A., et al. Quantum key distribution and beyond: introduction. JOSA B, 2019, 36 (3), P. QKD1–QKD2.Razavi M., Leverrier A., et al. Quantum key distribution and beyond: introduction. JOSA B, 2019, 36 (3), P. QKD1–QKD2.Ko H., Choi B.S., Choe J.S., Youn C.J. Advanced unambiguous state discrimination attack and countermeasure strategy in a practical B92 QKD system. Quantum Information Processing, 2018, 17 (17), P. 1–14.Ko H., Choi B.S., Choe J.S., Youn C.J. Advanced unambiguous state discrimination attack and countermeasure strategy in a practical B92 QKD system. Quantum Information Processing, 2018, 17 (17), P. 1–14.Ivanova A.E., Chivilikhin S.A., Gleim A.V. Quantum random number generator based on homodyne detection. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8 (2), P. 239–242.Ivanova A.E., Chivilikhin S.A., Gleim A.V. Quantum random number generator based on homodyne detection. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8 (2), P. 239–242.Ivanova A.E., Chivilikhin S.A., Gleim A.V. The use of beam and fiber splitters in quantum random number generators based on vacuum fluctuations. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (2), P. 378–383.Ivanova A.E., Chivilikhin S.A., Gleim A.V. The use of beam and fiber splitters in quantum random number generators based on vacuum fluctuations. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (2), P. 378–383.Ivanova A.E., Egorov V.I., Chivilikhin S.A., Gleim A.V. Investigation of quantum random number generation based on space-time division of photons. Nanosystems: Physics, Chemistry, Mathematics, 2013, 4 (4), P. 550–554.Ivanova A.E., Egorov V.I., Chivilikhin S.A., Gleim A.V. Investigation of quantum random number generation based on space-time division of photons. Nanosystems: Physics, Chemistry, Mathematics, 2013, 4 (4), P. 550–554.Barnett S.M., Croke S. Quantum state discrimination. Advances in Optics and Photonics, 2009, 1 (2), P. 238–278.Barnett S.M., Croke S. Quantum state discrimination. Advances in Optics and Photonics, 2009, 1 (2), P. 238–278.Peres A., Terno D.R. Optimal distinction between non-orthogonal quantum states. Journal of Physics A: Mathematical and General, 1998, 31 (34), P. 7105–7111.Peres A., Terno D.R. Optimal distinction between non-orthogonal quantum states. Journal of Physics A: Mathematical and General, 1998, 31 (34), P. 7105–7111.Chefles A., Barnett S.M. Optimum unambiguous discrimination between linearly independent symmetric states. Physics letters A, 1998, 250 (4–6), P. 223–229.Chefles A., Barnett S.M. Optimum unambiguous discrimination between linearly independent symmetric states. Physics letters A, 1998, 250 (4–6), P. 223–229.Chefles A. Unambiguous discrimination between linearly independent quantum states. Physics Letters A, 1998, 239 (6), P. 339–347.Chefles A. Unambiguous discrimination between linearly independent quantum states. Physics Letters A, 1998, 239 (6), P. 339–347.Zhang S., Feng Y., Sun X., Ying M. Upper bound for the success probability of unambiguous discrimination among quantum states. Physical Review A, 2001, 64 (6), 062103, P. 1–3.Zhang S., Feng Y., Sun X., Ying M. Upper bound for the success probability of unambiguous discrimination among quantum states. Physical Review A, 2001, 64 (6), 062103, P. 1–3.Duan L.M., Guo G.C. Probabilistic cloning and identification of linearly independent quantum states. Physical review letters, 1998, 80 (22), P. 4999–5002.Duan L.M., Guo G.C. Probabilistic cloning and identification of linearly independent quantum states. Physical review letters, 1998, 80 (22), P. 4999–5002.Sun X., Zhang S., Feng Y., Ying M. Mathematical nature of and a family of lower bounds for the success probability of unambiguous discrimination. Physical Review A, 2002, 65 (4), 044306, P. 1–3.Sun X., Zhang S., Feng Y., Ying M. Mathematical nature of and a family of lower bounds for the success probability of unambiguous discrimination. Physical Review A, 2002, 65 (4), 044306, P. 1–3.Eldar Y.C. A semidefinite programming approach to optimal unambiguous discrimination of quantum states. IEEE Transactions on information theory, 2003, 49 (2), P. 446–456.Eldar Y.C. A semidefinite programming approach to optimal unambiguous discrimination of quantum states. IEEE Transactions on information theory, 2003, 49 (2), P. 446–456.Galvao E.F., Hardy L. Cloning and quantum computation. Physical Review A, 2000, 62 (2), 022301, P. 1–5.Galvao E.F., Hardy L. Cloning and quantum computation. Physical Review A, 2000, 62 (2), 022301, P. 1–5.Chefles A., Kitagawa A., et al. Unambiguous discrimination among oracle operators. Journal of Physics A: Mathematical and Theoretical, 2007, 40 (33), P. 10183–10213.Chefles A., Kitagawa A., et al. Unambiguous discrimination among oracle operators. Journal of Physics A: Mathematical and Theoretical, 2007, 40 (33), P. 10183–10213.Jaeger G., Shimony A. Optimal distinction between two non-orthogonal quantum states. Physics Letters A, 1995, 197 (2), P. 83–87.Jaeger G., Shimony A. Optimal distinction between two non-orthogonal quantum states. Physics Letters A, 1995, 197 (2), P. 83–87.

The authors declare that there are no conflicts of interest present.