Refined finite-size analysis of binary-modulation continuous-variable quantum key distribution

Takaya Matsuura1,2, Shinichiro Yamano1, Yui Kuramochi3, Toshihiko Sasaki1,4, and Masato Koashi1,4

1Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
2Centre for Quantum Computation & Communication Technology, School of Science, RMIT University, Melbourne VIC 3000, Australia
3Department of Physics, Faculty of Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, Japan
4Photon Science Center, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

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Abstract

Recent studies showed the finite-size security of binary-modulation CV-QKD protocols against general attacks. However, they gave poor key-rate scaling against transmission distance. Here, we extend the security proof based on complementarity, which is used in the discrete-variable QKD, to the previously developed binary-modulation CV-QKD protocols with the reverse reconciliation under the finite-size regime and obtain large improvements in the key rates. Notably, the key rate in the asymptotic limit scales linearly against the attenuation rate, which is known to be optimal scaling but is not achieved in previous finite-size analyses. This refined security approach may offer full-fledged security proofs for other discrete-modulation CV-QKD protocols.

Continuous-variable (CV) quantum key distribution (QKD) has distinct advantages in the real-world implementation due to the established technologies for detectors and capability of large multiplexing. Its security proof is, however, difficult due to the continuous nature of the observables. To the best of authors' knowledge, the finite-size analysis that simultaneously achieves 1) security against general attacks, 2) composability, 3) compatibility with the discretization, and 4) asymptotically optimal scaling has not been known. A recently developed security proof of the binary-modulation CV-QKD protocol achieves 1)–3) above, but fails to achieve 4). Here, we remedy the situation by developing a refined security proof for the binary-modulation CV-QKD protocol based on the reverse reconciliation. This is realized by exploiting an asymmetry of eavesdropper's knowledge for the sender's and receiver's bit. With this refinement, the protocol achieves the expected performance in the limit of infinitely many repetitions, i.e., the requirement 4). This result may thus be a step towards complete security of the CV-QKD protocols.

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Cited by

[1] Yichen Zhang, Yiming Bian, Zhengyu Li, Song Yu, and Hong Guo, "Continuous-variable quantum key distribution system: Past, present, and future", Applied Physics Reviews 11 1, 011318 (2024).

[2] Shinichiro Yamano, Takaya Matsuura, Yui Kuramochi, Toshihiko Sasaki, and Masato Koashi, "General treatment of Gaussian trusted noise in continuous variable quantum key distribution", arXiv:2305.17684, (2023).

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