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Quantum Information and Measurement (QIM)

Composable security of two-way continuous-variable quantum key distribution without active symmetrization

Shouvik Ghorai, Eleni Diamanti, Anthony Leverrier

Published Jan 1, 2019• 4 citations
Publisher

Abstract

We present a general framework for CV-QKD protocols involving only a Gaussian modulation of coherent states and heterodyne detection. We exploit their symmetry in phase-space to obtain a composable security proof against general attacks.
DOI
10.1364/qim.2019.t5a.55

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We present a general framework encompassing a number of continuous-variable quantum key distribution protocols, including standard one-way protocols, measurement-device-independent protocols, as well as some two-way protocols, or any other continuous-variable protocol involving only a Gaussian modulation of coherent states and heterodyne detection. The main interest of this framework is that the corresponding protocols are all covariant with respect to the action of the unitary group U(n)\text{U}(n)U(n), implying that their security can be established thanks to a Gaussian de Finetti reduction. In particular, we give a composable security proof of two-way continuous-variable quantum key distribution against general attacks. We also prove that no active symmetrization procedure is required for these protocols, which would otherwise make them prohibitively costly to implement.
We present a general framework encompassing a number of continuous-variable quantum key distribution protocols, including standard one-way protocols, measurement-device-independent protocols as well as some two-way protocols, or any other continuous-variable protocol involving only a Gaussian modulation of coherent states and heterodyne detection. The main interest of this framework is that the corresponding protocols are all covariant with respect to the action of the unitary group U(n)U(n)U(n), implying that their security can be established thanks to a Gaussian de Finetti reduction. In particular, we give a composable security proof of two-way continuous-variable quantum key distribution against general attacks. We also prove that no active symmetrization procedure is required for these protocols, which would otherwise make them prohibitively costly to implement.
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.
Continuous variable (CV) quantum key distribution (QKD) provides a powerful setting for secure quantum communications, thanks to the use of room-temperature off-the-shelf optical devices and the potential to reach much higher rates than the standard discrete-variable counterpart. In this paper, we provide a general framework for studying the composable finite-size security of CV-QKD with Gaussian-modulated coherent-state protocols under various levels of trust for the loss and noise experienced by the parties. Our paper considers both wired (i.e., fiber-based) and wireless (i.e., free-space) quantum communications. In the latter case, we show that high key rates are achievable for short-range optical wireless (LiFi) in secure quantum networks with both fixed and mobile devices. Finally, we extend our investigation to microwave wireless (WiFi) discussing security and feasibility of CV-QKD for very short-range applications.
Discretely modulated continuous-variables quantum key distribution (CV-QKD) protocols are usually proposed with phase modulated coherent states being sent by Alice and simple homodyne detection on the Bob side and, in the majority of the studies, their security is analyzed assuming that for low photon number the protocols are similar to a Gaussian modulated CV-QKD. Here we discuss other detection techniques such as double homodyne, consider classical attacks and find practical strategies for the legitimate parties to reach the security limits predicted by the Gaussian modulated CV-QKD.