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Quantum key distribution with non-ideal heterodyne detection

Cosmo Lupo, Yingkai Ouyang

Published Aug 1, 2021• 0 citations
OpenAlex

Abstract

Continuous-variable quantum key distribution exploits coherent measurements of the electromagnetic field, i.e., homodyne or heterodyne detection. The most advanced security analyses developed so far relied on idealised mathematical models for such measurements, which assume that the measurement outcomes are continuous and unbounded variables. As any physical measurement device has finite range and precision, these mathematical models only serve as an approximation. It is expected that, under suitable conditions, the predictions obtained using these simplified models are in good agreement with the actual experimental implementations. However, a quantitative analysis of the error introduced by this approximation, and of its impact on composable security, have been lacking so far. Here we present a theory to rigorously account for the experimental limitations of realistic heterodyne detection. We focus on asymptotic security against collective attacks, and indicate a route to include finite-size effects.

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Continuous-variable quantum key distribution exploits coherent measurements of the electromagnetic field, i.e., homodyne or heterodyne detection. The most advanced security analyses developed so far relied on idealised mathematical models for such measurements, which assume that the measurement outcomes are continuous and unbounded variables. As any physical measurement device has finite range and precision, these mathematical models only serve as an approximation. It is expected that, under suitable conditions, the predictions obtained using these simplified models are in good agreement with the actual experimental implementations. However, a quantitative analysis of the error introduced by this approximation, and of its impact on composable security, have been lacking so far. Here we present a theory to rigorously account for the experimental limitations of realistic heterodyne detection. We focus on asymptotic security against collective attacks, and indicate a route to include finite-size effects.
Continuous-variable quantum key distribution (CV-QKD) using coherent states and heterodyne detection enables secure quantum communication based on technology that has large similarities to coherent optical telecommunication. Yet, practical implementations of coherent receivers used in both technologies encounter device imperfections, which for CV-QKD are often not addressed in security proofs. Here, we present a theoretical framework that rigorously accounts for imperfect heterodyne measurements arising from phase and amplitude imbalances in the coherent (heterodyne) receiver. Focusing on collective attacks, we establish a finite-size security proof that reveals how measurement imperfections limit the distance over which a positive key rate is achievable. To mitigate these effects, we propose a local transformation during classical post-processing. We validate our approach experimentally on a CV-QKD system with an imperfect coherent receiver, underscoring its potential for scalable, cost-effective CV-QKD with photonic integrated receivers in which phase and amplitude imbalances naturally appear through manufacturing tolerances.
In comparison to conventional discrete-variable (DV) quantum key distribution (QKD), continuous-variable (CV) QKD with homodyne/heterodyne measurements has distinct advantages of lower-cost implementation and affinity to wavelength division multiplexing. On the other hand, its continuous nature makes it harder to accommodate to practical signal processing, which is always discretized, leading to lack of complete security proofs so far. Here we propose a tight and robust method of estimating fidelity of an optical pulse to a coherent state via heterodyne measurements. We then construct a binary phase modulated CV-QKD protocol and prove its security in the finite-key-size regime against general coherent attacks, based on proof techniques of DV QKD. Such a complete security proof is indispensable for exploiting the benefits of CV QKD.
Abstract In comparison to conventional discrete-variable (DV) quantum key distribution (QKD), continuous-variable (CV) QKD with homodyne/heterodyne measurements has distinct advantages of lower-cost implementation and affinity to wavelength division multiplexing. On the other hand, its continuous nature makes it harder to accommodate to practical signal processing, which is always discretized, leading to lack of complete security proofs so far. Here we propose a tight and robust method of estimating fidelity of an optical pulse to a coherent state via heterodyne measurements. We then construct a binary phase modulated CV-QKD protocol and prove its security in the finite-key-size regime against general coherent attacks, based on proof techniques of DV QKD. Such a complete security proof is indispensable for exploiting the benefits of CV QKD.
Continuous-variable quantum key distribution protocol using coherent states and heterodyne detection, called the no-switching protocol, is widely used in practical systems due to the simple experimental setup without basis switching and easy assessment to phase information. The security of an ideal no-switching protocol has been proved against general attacks in the finite-size regime and composable security framework, whose heterodyne detector consists of a beam splitter with transmittance of $50\mathrm{%}$ and two ideal homodyne detectors. However, the transmittance of a beam splitter is inaccurate and the two detectors always have different quantum efficiency and electronic noise, which introduce asymmetry into the heterodyne detection, and further lead to the mismatch between the ideal protocol and practical systems, thereby overestimating the secret key rate and resulting in a practical security loophole. In this paper, we close this loophole by proposing a modified no-switching protocol with biased quadrature detection, where the asymmetry of the heterodyne detection is modeled to match the practical systems, and the security of the protocol is analyzed in asymptotic and finite-size regimes. Further, an optimization strategy is proposed to achieve the optimal secret key rate by adjusting the transmittance of the beam splitter. Simulation results show the necessity of considering the asymmetry in heterodyne detection and the effectiveness of the optimization, which provides a promising way to realize a practical secure and high-performance no-switching system.
We provide a security analysis for continuous variable quantum key distribution protocols based on the transmission of two-mode squeezed vacuum states measured via homodyne detection. We employ a version of the entropic uncertainty relation for smooth entropies to give a lower bound on the number of secret bits which can be extracted from a finite number of runs of the protocol. This bound is valid under general coherent attacks, and gives rise to keys which are composably secure. For comparison, we also give a lower bound valid under the assumption of collective attacks. For both scenarios, we find positive key rates using experimental parameters reachable today.