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Continuous variable subcarrier wave 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 Oct 10, 2019• 0 citations
OpenAlex

Abstract

In this paper we propose a continuous-variable subcarrier wave quantum key distribution scheme with homodyne detection and present its security analysis in the finite-size regime. 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 a secret keys over channels with losses up to 9 dB.

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•Feb 4, 2019•0 citations
In this paper we propose a continuous-variable subcarrier wave quantum key distribution scheme with homodyne detection and present its security analysis in the finite-size regime. 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 a secret keys over channels with losses up to 9 dB.
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.
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.
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.
This paper introduces an approach to solving the convex optimization problem for subcarrier wave continuous-variable quantum key distribution (QKD) protocol using discrete modulation. For the first time, we provide a solution to this problem. By employing semidefinite programming, we have estimated the lower bound of the secure key generation rate in the asymptotic limit, taking into account an optimal attack from potential eavesdroppers. We considered an optical scheme that involves the use of quadrature phase modulation of coherent states and coherent detection based on the interference between the carrier and side frequencies. Our findings demonstrate the feasibility of distributing secure key generation rates over distances exceeding 100 km, even in the presence of realistic excess noise.
Quantum conditional entropies play a fundamental role in quantum information theory. In quantum key distribution, they are exploited to obtain reliable lower bounds on the secret-key rates in the finite-size regime, against collective attacks and coherent attacks under suitable assumptions. Here we consider continuous-variable communication protocols, where the sender Alice encodes information using a discrete modulation of phase-shifted coherent states, and the receiver Bob decodes by homodyne or heterodyne detection. We compute the Petz-Rényi and sandwiched Rényi conditional entropies associated with these setups, assuming either a passive eavesdropper or one that injects thermal photons into the channel, who gathers the quantum information leaked through a lossy communication line of known or bounded transmittance. Whereas our results do not directly provide reliable key-rate estimates, they do represent useful ballpark figures. We obtain analytical or semianalytical expressions that do not require intensive numerical calculations. These expressions serve as bounds on the key rates that may be tight in certain scenarios. We compare different estimates, including known bounds that have already appeared in the literature and bounds that we determine. The latter are found to be tighter for very short block sizes.
We establish a lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with a discrete modulation of coherent states. The bound is valid against collective attacks and is obtained by formulating the problem as a semidefinite program. We illustrate our general approach with the quadrature phase-shift keying (QPSK) modulation scheme and show that distances over 100 km are achievable for realistic values of noise. We also discuss the application to more complex quadrature amplitude modulations (QAM) schemes. This work is a major step towards establishing the full security of continuous-variable protocols with a discrete modulation in the finite-size regime and opens the way to large-scale deployment of these protocols for quantum key distribution.