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arXiv:1910.04431 · Scientific Reports

Subcarrier wave continuous variable quantum key distribution with discrete modulation: mathematical model and finite-key analysis

E.O. Samsonov, R. Goncharov, Andrei Gaidash, Козубов Антон Владимирович, V. I. Egorov, Artur V. Gleim

Published Jun 22, 2020• 37 citations
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Abstract

In this paper we report a continuous-variable quantum key distribution protocol using multimode coherent states generated on subcarrier frequencies of the optical spectrum. We propose a coherent detection scheme where power from a carrier wave is used as a local oscillator. We compose a mathematical model of the proposed scheme and perform its security analysis in the finite-size regime using fully quantum asymptotic equipartition property technique. We calculate a lower bound on the secret key rate for the system under the assumption that the quantum channel noise is negligible compared to detector dark counts, and an eavesdropper is restricted to collective attacks. Our calculation shows that the current realistic system implementation would allow distributing secret keys over channels with losses up to 9 dB.

DOI
10.1038/s41598-020-66948-0

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In this paper, we continue the study of the quantum cryptographic GG02 protocol, performed using the approach based on the subcarrier waves. We modify the scheme via heterodyne detection and perform security analysis for the full trusted hardware noise model in the presence of collective attacks with finite-key effects. It is shown that the system can potentially distribute the key even if the level of losses in the channel is above 9 dB. This result is consistent with the general technical level and comply with modern standards of practical CV-QKD systems. Finally, the system under consideration fully meets the criterion of composability.
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Abstract The aim of the paper is to describe a well-known quantum key distribution GG02 protocol using multimode coherent states generated on subcarrier frequencies of the optical spectrum. In order to detect signal states, we use a method of coherent detection without the participation of a local oscillator directly but where power from a carrier wave is used as such. Within the framework of the modern GG02 protocol description and the secutity proof against collective attacks, we introduce the necessary amendments to reduce our model to a model of the common system.
We consider discrete-modulation protocols for continuous-variable quantum key distribution (CV-QKD) that employ a modulation constellation consisting of a finite number of coherent states and that use a homodyne- or a heterodyne-detection receiver. We establish a security proof for collective attacks in the asymptotic regime, and we provide a formula for an achievable secret-key rate. Previous works established security proofs for discrete-modulation CV-QKD protocols that use two or three coherent states. The main constituents of our approach include approximating a complex, isotropic Gaussian probability distribution by a finite-size Gauss-Hermite constellation, applying entropic continuity bounds, and leveraging previous security proofs for Gaussian-modulation protocols. As an application of our method, we calculate secret-key rates achievable over a lossy thermal bosonic channel. We show that the rates for discrete-modulation protocols approach the rates achieved by a Gaussian-modulation protocol as the constellation size is increased. For pure-loss channels, our results indicate that in the high-loss regime and for sufficiently large constellation size, the achievable key rates scale optimally, i.e., proportional to the channel's transmissivity.