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arXiv:1711.09039

Security of Continuous-Variable Quantum Key Distribution with Discrete Modulation against General Attacks

Jian Zhou, Ying Guo, Duan Huang, Guihua Zeng

Published Nov 22, 2017• 1 citation
arXivHTMLPDF

Abstract

We provide a security analysis of continuous-variable quantum key distribution (CVQKD) with discrete modulation against general attacks in a realistic finite-size regime. To realize this goal, we first prove security of the continuous-variable quantum key distribution protocol with discrete modulation against collective attacks by using the reliable tomography of the covariance matrix, leading to the reliable and tight error bounds in the derived confidence regions. Combining the proof with de Finetti reduction, the discrete-modulation-based continuous-variable quantum key distribution (DM-CVQKD) is proved to be secure even exposing to general attacks. Specially, we use an energy test to truncate the Hilbert space globally to provide security.

DOI
10.48550/arxiv.1711.09039

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We provide a security analysis of continuous-variable quantum key distribution (CVQKD) with discrete modulation against general attacks in a realistic finite-size regime. To realize this goal, we first prove security of the continuous-variable quantum key distribution protocol with discrete modulation against collective attacks by using the reliable tomography of the covariance matrix, leading to the reliable and tight error bounds in the derived confidence regions. Combining the proof with de Finetti reduction, the discrete-modulation-based continuous-variable quantum key distribution (DM-CVQKD) is proved to be secure even exposing to general attacks. Specially, we use an energy test to truncate the Hilbert space globally to provide security.
Discrete-modulated (DM) continuous-variable quantum key distribution (CV-QKD) protocols are promising candidates for commercial implementations of quantum communication networks due to their experimental simplicity.While tight security analyses in the asymptotic limit exist, proofs in the finitesize regime are still subject to active research.We present a composable finite-size security proof against independently and identically distributed collective attacks for a general DM CV-QKD protocol.We introduce a new energy testing theorem to bound the effective dimension of Bob's system and rigorously prove security within Renner's -security framework and address the issue of acceptance sets in protocols and their security proof.We want to highlight that our method also allows for nonunique acceptance statistics, which is necessary in practise.Finally, we extend and apply a numerical security proof technique to calculate tight lower bounds on the secure key rate.To demonstrate our method, we apply it to a quadrature phase-shift keying protocol for both untrusted, ideal and trusted, nonideal detectors.The results show that our security proof method yields secure finite-size key rates under experimentally viable conditions up to at least 72 km transmission distance.
In recent years, discrete-modulated continuous-variable quantum key distribution (DM-CV-QKD) has gained traction due to its practical advantages: cost-effectiveness, simple state preparation, and compatibility with existing communication technologies. This work presents a security analysis of DM-CV-QKD against general sequential attacks, including finite-size effects. Remarkably, our proof considers attacks that are neither independent nor identical, and makes no assumptions about the Hilbert space dimension of the receiver. To analyse the security, we leverage the recent generalised entropy accumulation theorem and the numerical methods based on quasi-relative entropy. We also develop a novel dimension reduction technique which is compatible with the entropy accumulation framework. While our analysis reveals significant finite-size corrections to the key rate, the protocol might still offer advantages in specific scenarios due to its practical merits. Our work also offers some insights on how future security proofs can improve the security bounds derived in this work.
Continuous variable quantum key distribution via discrete modulations ensures information-theoretic security using standard telecom technologies, providing affordable and scalable quantum communications with simplified classical postprocessing. However, existing security proofs against general attacks often rely on restrictive assumptions, such as a bounded dimension for coherent states, or require impractically large block sizes. In this work, we develop a finite-size security analysis that removes these limitations while incorporating realistic experimental features. Our approach combines an optimization under infinite dimensions, a security proof against general attacks, a trusted detector model accounting for the receiver imperfections, and postselection strategies to reuse discarded measurement outcomes. We report positive key rates in the finite-size regime for relevant block sizes of the order of 10710^7107. These results contribute to narrowing the gap between theoretical security proofs and practical implementations of discrete-modulated continuous variable quantum key distribution protocols.
The discretely modulated continuous-variable quantum key distribution (DM CVQKD) has been proven to be secure, and a basic assumption for the current theoretical security proof of the DM CVQKD is that the signal source cannot be compromised. However, this assumption is quite unpractical in real quantum communication systems. In this paper, we investigate the DM CVQKD with a special configuration in which the entanglement source is placed at the untrusted channel. With this configuration, the source is no longer protected by the sender but is exposed to the vulnerable environment. In particular, we consider the configuration for two typical DM CVQKD protocols, which are the four-state protocol and the eight-state protocol. Security analysis based on linear bosonic channel shows that the DM CVQKD with an untrusted entanglement source is able to defend itself against the most powerful quantum collective attack in a certain distance range and it can still generate positive secret key rate when considering finite-size effect and composable security, thereby providing a theoretical proof for applying the DM CVQKD system to a realistic environment.
Establishing the security of continuous-variable quantum key distribution against general attacks in a realistic finite-size regime is an outstanding open problem in the field of theoretical quantum cryptography if we restrict our attention to protocols that rely on the exchange of coherent states. Indeed, techniques based on the uncertainty principle are not known to work for such protocols, and the usual tools based on de Finetti reductions only provide security for unrealistically large block lengths. We address this problem here by considering a new type of Gaussian de Finetti reduction, that exploits the invariance of some continuous-variable protocols under the action of the unitary group U(n) (instead of the symmetric group S_{n} as in usual de Finetti theorems), and by introducing generalized SU(2,2) coherent states. Crucially, combined with an energy test, this allows us to truncate the Hilbert space globally instead as at the single-mode level as in previous approaches that failed to provide security in realistic conditions. Our reduction shows that it is sufficient to prove the security of these protocols against Gaussian collective attacks in order to obtain security against general attacks, thereby confirming rigorously the widely held belief that Gaussian attacks are indeed optimal against such protocols.
Continuous variable quantum key distribution with discrete modulation has the potential to provide information-theoretic security using widely available optical elements and existing telecom infrastructure. While their implementation is significantly simpler than that for protocols based on Gaussian modulation, proving their finite-size security against coherent attacks poses a challenge. In this work we prove finite-size security against coherent attacks for a discrete-modulated quantum key distribution protocol involving four coherent states and heterodyne detection. To do so, and contrary to most of the existing schemes, we first discretize all the continuous variables generated during the protocol. This allows us to use the entropy accumulation theorem, a tool that has previously been used in the setting of discrete variables, to construct the finite-size security proof. We then compute the corresponding finite-key rates through semi-definite programming and under a photon-number cutoff. Our analysis provides asymptotic rates in the range of 0.1 − 10 − 4 bits per round for distances up to hundred kilometres, while in the finite case and for realistic parameters, we get of the order of 10 Gbits of secret key after n ∼ 10 11 rounds and distances of few tens of kilometres.