najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2021-12-6-697-702najo-555Research ArticlePHYSICSФИЗИКАDiscrimination and decoherence of Schrödinger cat states in lossy quantum channelsДискриминация и декогеренция состояний кота Шредингера в квантовых каналах с потерямиGoncharovR. K.GoncharovR. K.

3, Kadetskaya Line, 199034 Saint Petersburg.

rkgoncharov@itmo.ruKiselevA. D.KiselevA. D.

3, Kadetskaya Line, 199034 Saint Petersburg.

VeselkovaN. G.VeselkovaN. G.

3, Kadetskaya Line, 199034 Saint Petersburg

AliRanimAliRanim

49, bldg. A, Kronverksky Pr., 197101 Saint Petersburg.

KiselevF. D.KiselevF. D.

3, Kadetskaya Line, 199034 Saint Petersburg.

Quantum Information Laboratory, ITMO University; Laboratory of Quantum Processes and Measurements, ITMO UniversityRussian FederationQuantum Information Laboratory, ITMO UniversityRussian FederationFaculty of Photonics, ITMO UniversityRussian Federation202107082025126697702Copyright © Goncharov R.K., Kiselev A.D., Veselkova N.G., Ali R., Kiselev F.D., 20252025Goncharov R.K., Kiselev A.D., Veselkova N.G., Ali R., Kiselev F.D.Goncharov R.K., Kiselev A.D., Veselkova N.G., Ali R., Kiselev F.D.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/555

We investigate environment induced effects of decoherence in discrimination between the Schrödinger cat states transmitted through noisy quantum¨ channels such as optical fibers. We calculate the fidelity and the statistics of photocounts for both even and odd coherent states. The method that uses the beam splitter-like transformation acting in the enlarged Hilbert space to model the quantum channel is compared with the approach based on the Lindblad dynamics of one-mode bosonic systems.

Мы исследуем вызванные окружающей средой эффекты декогеренции при различении состояний кота Шредингера, передаваемых через зашумленные квантовые каналы, такие как оптические волокна. Мы рассчитываем точность и статистику фотоотсчетов как для четных, так и для нечетных когерентных состояний. Метод, использующий светоделительное преобразование, действующее в расширенном гильбертовом пространстве, для моделирования квантового канала сравнивается с подходом, основанным на динамике Линдблада одномодовых бозонных систем.

состояния кота Шредингерадекогеренцияразличение квантовых состоянийSchrödinger cat statesdecoherencequantum state discriminationThe work was done by Leading Research Center “National Center of Quantum Internet” of ITMO University during the implementation of the government support program, with the financial support of Ministry of Digital Development, Communications and Mass Media of the Russian Federation and RVC JSC; Grant Agreement ID: 0000000007119P190002, agreement No. 006-20 dated 27.03.2020. A.D.K. acknowledges financial support by the Ministry of Education and Science of the Russian Federation (Grant No. 2019-0903).ReferencesDodonov V.V., Malkin I.A., Man’ko V.I. Even and odd coherent states and excitations of a singular oscillator, Physica, 1974, 72(3), P. 597–615.Dodonov V.V., Malkin I.A., Man’ko V.I. Even and odd coherent states and excitations of a singular oscillator, Physica, 1974, 72(3), P. 597–615.Hao L., Tang H., Wang Q. Resolution improvement of angular rotation measurement through even coherent states coupled with parity detection strategy. Journal of Optics, 2020, 22(2), P. 025203.Hao L., Tang H., Wang Q. Resolution improvement of angular rotation measurement through even coherent states coupled with parity detection strategy. Journal of Optics, 2020, 22(2), P. 025203.Lund A.P., Ralph T.C., Haselgrove H.L. Fault-tolerant linear optical quantum computing with small-amplitude coherent states. Phys. Rev. Lett., 2008, 100, P. 030503.Lund A.P., Ralph T.C., Haselgrove H.L. Fault-tolerant linear optical quantum computing with small-amplitude coherent states. Phys. Rev. Lett., 2008, 100, P. 030503.Sangouard N., Simon C., Gisin N., Laurat J., Tualle-Brouri R., Grangier P. Quantum repeaters with entangled coherent states. J. Opt. Soc. Am. B, 2010, 27(6), P. A137–A145.Sangouard N., Simon C., Gisin N., Laurat J., Tualle-Brouri R., Grangier P. Quantum repeaters with entangled coherent states. J. Opt. Soc. Am. B, 2010, 27(6), P. A137–A145.Brask J.B., Rigas I., Polzik E.S., Andersen U.L., Sørensen A.S. Hybrid long-distance entanglement distribution protocol. Phys. Rev. Lett., 2010, 105, P. 160501.Brask J.B., Rigas I., Polzik E.S., Andersen U.L., Sørensen A.S. Hybrid long-distance entanglement distribution protocol. Phys. Rev. Lett., 2010, 105, P. 160501.Ghasemi M., Tavassoly M.K. Toward a quantum repeater protocol based on the coherent state approach. Laser Physics, 2019, 29.Ghasemi M., Tavassoly M.K. Toward a quantum repeater protocol based on the coherent state approach. Laser Physics, 2019, 29.Parker R.C., Joo J., Spiller T.P. Photonic hybrid state entanglement swapping using cat state superpositions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2020, 476(2243), P. 20200237.Parker R.C., Joo J., Spiller T.P. Photonic hybrid state entanglement swapping using cat state superpositions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2020, 476(2243), P. 20200237.Yurke B., Stoler D. Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion. Phys. Rev. Lett., 1986, 57, P. 13–16.Yurke B., Stoler D. Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion. Phys. Rev. Lett., 1986, 57, P. 13–16.Neergaard-Nielsen J.S., Nielsen B.M., Hettich C., Mølmer K., Polzik E.S., Generation of a superposition of odd photon number states for quantum information networks. Phys. Rev. Lett., 2006, 97, P. 083604.Neergaard-Nielsen J.S., Nielsen B.M., Hettich C., Mølmer K., Polzik E.S., Generation of a superposition of odd photon number states for quantum information networks. Phys. Rev. Lett., 2006, 97, P. 083604.Ourjoumtsev A., Ferreyrol F., Tualle-Brouri R., Grangier P. Preparation of non-local superpositions of quasi-classical light states. Nature Physics, 2009, 5, P. 189–192.Ourjoumtsev A., Ferreyrol F., Tualle-Brouri R., Grangier P. Preparation of non-local superpositions of quasi-classical light states. Nature Physics, 2009, 5, P. 189–192.Serikawa T., Yoshikawa J.-i., Takeda S., Yonezawa H., Ralph T.C., Huntington E.H., Furusawa A. Generation of a cat state in an optical sideband. Phys. Rev. Lett., 2018, 121, P. 143602.Serikawa T., Yoshikawa J.-i., Takeda S., Yonezawa H., Ralph T.C., Huntington E.H., Furusawa A. Generation of a cat state in an optical sideband. Phys. Rev. Lett., 2018, 121, P. 143602.Takase K., Yoshikawa J.-i., Asavanant W., Endo M., Furusawa A. Generation of optical Schrodinger cat states by generalized photon subtrac-¨ tion. Phys. Rev. A, 2021, 103, P. 013710.Takase K., Yoshikawa J.-i., Asavanant W., Endo M., Furusawa A. Generation of optical Schrodinger cat states by generalized photon subtrac-¨ tion. Phys. Rev. A, 2021, 103, P. 013710.Ourjoumtsev A., Jeong H., Tualle-Brouri R., Grangier P. Generation of optical “Schrodinger cats” from photon number states.¨ Nature, 2007, 448, P. 784–786.Ourjoumtsev A., Jeong H., Tualle-Brouri R., Grangier P. Generation of optical “Schrodinger cats” from photon number states.¨ Nature, 2007, 448, P. 784–786.Glancy S., de Vasconcelos H.M. Methods for producing optical coherent state superpositions. J. Opt. Soc. Am. B, 2008, 25(5), P. 712–733.Glancy S., de Vasconcelos H.M. Methods for producing optical coherent state superpositions. J. Opt. Soc. Am. B, 2008, 25(5), P. 712–733.S.J. van Enk, Hirota O. Entangled coherent states: Teleportation and decoherence. Phys. Rev. A, 2001, 64, P. 022313.S.J. van Enk, Hirota O. Entangled coherent states: Teleportation and decoherence. Phys. Rev. A, 2001, 64, P. 022313.Miroshnichenko G.P., Kiselev A.D., Trifanov A.I., Gleim A.V. Algebraic approach to electro-optic modulation of light: exactly solvable multimode quantum model. J. Opt. Soc. Am. B, 2017, 34(6), P. 1177–1190.Miroshnichenko G.P., Kiselev A.D., Trifanov A.I., Gleim A.V. Algebraic approach to electro-optic modulation of light: exactly solvable multimode quantum model. J. Opt. Soc. Am. B, 2017, 34(6), P. 1177–1190.Kelley P.L., Kleiner W.H. Theory of electromagnetic field measurement and photoelectron counting. Phys. Rev., 1964, 136, P. A316–A334.Kelley P.L., Kleiner W.H. Theory of electromagnetic field measurement and photoelectron counting. Phys. Rev., 1964, 136, P. A316–A334.Kozubov A., Gaidash A., Miroshnichenko G. Quantum model of decoherence in the polarization domain for the fiber channel. Phys. Rev. A, 2019, 99, P. 053842.Kozubov A., Gaidash A., Miroshnichenko G. Quantum model of decoherence in the polarization domain for the fiber channel. Phys. Rev. A, 2019, 99, P. 053842.Gaidash A., Kozubov A., Miroshnichenko G. Dissipative dynamics of quantum states in the fiber channel. Phys. Rev. A, 2020, 102, P. 023711.Gaidash A., Kozubov A., Miroshnichenko G. Dissipative dynamics of quantum states in the fiber channel. Phys. Rev. A, 2020, 102, P. 023711.Kiselev A.D., Ali R., Rybin A.V. Lindblad dynamics and disentanglement in multi-mode bosonic systems. Entropy, 2021, 23(11).Kiselev A.D., Ali R., Rybin A.V. Lindblad dynamics and disentanglement in multi-mode bosonic systems. Entropy, 2021, 23(11).

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