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arXiv:2008.03510 · Physical Review Research

Tight finite-key analysis for generalized high-dimensional quantum key distribution

Rong Wang, Zhen-Qiang Yin, Hang Liu, Shuang Wang, Wei Chen, Guang-Can Guo, Zheng-Fu Han

Published Apr 7, 2021• 10 citations
arXivHTMLPDF

Abstract

Due to the capability of tolerating high error rate and generating more key bits per trial, high-dimensional quantum key distribution attracts wide interest.Despite great progresses in high-dimensional quantum key distribution, there are still some gaps between theory and experiment.One of these is that the security of the secret key heavily depends on the number of the emitted signals.So far, the existing security proofs are only suitable in the case with an infinite or unpractically large number of emitted signals.Here, by introducing the idea of "key classification" and developing relevant techniques based on the uncertainty relation for smooth entropies, we propose a tight finite-key analysis suitable for generalized high-dimensional quantum key distribution protocols.Benefitting from our theory, high-dimensional quantum key distribution protocols with finite resources become experimentally feasible.

DOI
10.1103/physrevresearch.3.023019

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Due to the capability of tolerating high error rate and generating more key bits per trial, high-dimensional quantum key distribution attracts wide interest.Despite great progresses in high-dimensional quantum key distribution, there are still some gaps between theory and experiment.One of these is that the security of the secret key heavily depends on the number of the emitted signals.So far, the existing security proofs are only suitable in the case with an infinite or unpractically large number of emitted signals.Here, by introducing the idea of "key classification" and developing relevant techniques based on the uncertainty relation for smooth entropies, we propose a tight finite-key analysis suitable for generalized high-dimensional quantum key distribution protocols.Benefitting from our theory, high-dimensional quantum key distribution protocols with finite resources become experimentally feasible.
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It has been shown recently that the framework of quantum sampling, as introduced by Bouman and Fehr, can lead to new entropic uncertainty relations highly applicable to finite-key cryptographic analyses. Here we revisit these so-called sampling-based entropic uncertainty relations, deriving newer, more powerful, relations and applying them to source-independent quantum random number generators and high-dimensional quantum key distribution protocols. Along the way, we prove several interesting results in the asymptotic case for our entropic uncertainty relations. These sampling-based approaches to entropic uncertainty, and their application to quantum cryptography, hold great potential for deriving proofs of security for quantum cryptographic systems, and the approaches we use here may be applicable to an even wider range of scenarios.
Quantum key distribution (QKD) can be proved to be secure by laws of quantum mechanics. In this thesis, we review security proof methods in Renner's framework and discuss numerical methods to calculate asymptotic and finite key rates. These methods are highly versatile and applicable to general device-dependent QKD protocols. We also discuss analytical tools that extend the applicability of these numerical methods. We then present the asymptotic security proof against collective attacks for a variant of the twin-field QKD protocol, which can overcome the repeaterless secret-key capacity bound. Our variant reduces the sifting cost and uses non-phase-randomized coherent states as both signals and test states. We confirm the loss scaling of this protocol. Another important family of protocols that we investigate here are discrete-modulated continuous-variable QKD protocols. They are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks. Our security proof method can provide tight asymptotic key rates. We demonstrate that the postselection of data in combination with reverse reconciliation can improve the key rates. We analyze both untrusted and trusted detector noise scenarios. Our results in the trusted detector noise scenario show that we can thus cut out most of the effect of detector noise and obtain asymptotic key rates similar to those had we access to ideal detectors. Finally, we present several simple examples to illustrate our newly developed method for the numerical finite-key analysis against the most general attacks via the entropy accumulation theorem.
Abstract Quantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments, however, predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite-key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime in terms of two semi-definite programs (SDPs). The first uses the relation between conditional smooth min-entropy and quantum relative entropy through the quantum asymptotic equipartition property, and the second uses the relation between the smooth min-entropy and quantum fidelity. The numerical programs are formulated under the assumption of collective attacks from the eavesdropper and can be promoted to withstand coherent attacks using the postselection technique. We then solve these SDPs using convex optimization solvers and obtain numerical calculations of finite-key rates for several protocols difficult to analyze analytically, such as BB84 with unequal detector efficiencies, B92, and twin-field QKD. Our numerical approach democratizes the composable security proofs for QKD protocols where the derived keys can be used as an input to another cryptosystem.
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Quantum Key Distribution is one of the most mature quantum protocols. This technological advancement comes with a need for new security proofs that work with realistic devices and perform well in the finite-size regime, where the users exchange a large but finite set of messages. In recent years, we have seen a new generation of proof techniques utilizing ideas from convex optimization or information theory. In this talk, I will present these new ideas and review some challenges and opportunities for the future work.