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Decoy States and Low-Density Parity-Check Error-Correcting Codes in Quantum Cryptography with Phase–Time Coding

  • ATOMS, MOLECULES, OPTICS
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Abstract

The cryptographic robustness of quantum key distribution (QKD) with phase–time coding against a photon number splitting (PNS) attack is analyzed. The line length up to which a secret key distribution is guaranteed is determined both by the protocol itself and by the efficiency of error correction in raw keys. The effect of different parameters of avalanche single-photon detectors on the length of the secret key distribution line is investigated. To correct errors, various versions of low-density parity-check (LDPC) codes are considered whose efficiency today is the closest to the Shannon theoretical limit.

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Notes

  1. Note that state (1) is a single-mode, formally infinitely large state. In a real situation, one uses packages localized in a time window with characteristic length of about 1 ns and spectrum width of 109 Hz. Since optical elements in quantum cryptography systems are almost linear and dispersionless (components of states with different frequencies are transformed identically) in this range, it suffices to consider states with a single wavelength.

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ACKNOWLEDGMENTS

One of the authors (S.N.M.) is grateful to his colleagues from the Academy of Cryptography of the Russian Federation for discussions. We are grateful to I.M. Arbekov, K.A. Balygin, A.N. Klimov, K.S. Kravtsov, and S.P. Kulik for numerous and intensive discussions, as well as to I.M. Arbekov and S.P. Kulik for reading the manuscript and a number of comments that helped improve the text.

Funding

This study was supported by the Russian Science Foundation (project no. 16-12-00015 (continuation)).

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Authors and Affiliations

  1. Faculty of Physics, Lomonosov Moscow State University, 119899, Moscow, Russia

    I. V. Sinil’shchikov

  2. Institute of Solid State Physics, Russian Academy of Sciences, 142432, Chernogolovka, Moscow oblast, Russia

    S. N. Molotkov

  3. Academy of Cryptography of the Russian Federation, 121552, Moscow, Russia

    S. N. Molotkov

  4. Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119899, Moscow, Russia

    S. N. Molotkov

  5. Quantum Technologies Center, Moscow State University, 119899, Moscow, Russia

    I. V. Sinil’shchikov & S. N. Molotkov

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  1. I. V. Sinil’shchikov
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Correspondence to S. N. Molotkov.

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Translated by I. Nikitin

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Sinil’shchikov, I.V., Molotkov, S.N. Decoy States and Low-Density Parity-Check Error-Correcting Codes in Quantum Cryptography with Phase–Time Coding. J. Exp. Theor. Phys. 129, 168–196 (2019). https://doi.org/10.1134/S1063776119070124

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  • DOI: https://doi.org/10.1134/S1063776119070124

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