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IEEE Transactions on Information Theory

Quantum Sampling for Finite Key Rates in High Dimensional Quantum Cryptography

Keegan Yao, Walter O. Krawec, Jiadong Zhu

Published Jan 11, 2022• 19 citations
Publisher

Abstract

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.

DOI
10.1109/tit.2022.3141874

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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.
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.
Entropic Uncertainty relations are powerful tools, especially in quantum cryptography. They typically bound the amount of uncertainty a third-party adversary may hold on a measurement outcome as a result of the measurement overlap. However, when the two measurement bases are biased towards one another, standard entropic uncertainty relations do not always provide optimal lower bounds on the entropy. Here, we derive a new entropic uncertainty relation, for certain quantum states, which can provide a significantly higher bound even if the two measurement bases are no longer mutually unbiased. We evaluate our bound on two different quantum cryptographic protocols, including BB84 with faulty/biased measurement devices, and show that our new bound can produce substantially higher key-rates under several scenarios when compared with prior work using standard entropic uncertainty relations.
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.
Abstract Two‐way quantum key distribution (QKD) protocols utilize bi‐directional quantum communication to establish a shared secret key. Due to the increased attack surface, security analyses remain challenging. Here a high‐dimensional variant of the Ping Pong protocol is investigated and an information theoretic security analysis in the finite‐key setting is performed. The main contribution in this work is to show a new proof methodology for two‐way quantum key distribution protocols based on the quantum sampling framework of Bouman and Fehr introduced in 2010 and also sampling‐based entropic uncertainty relations introduced by the authors in 2019. The Ping Pong protocol is only investigated here, but these methods may be broadly applicable to other QKD protocols, especially those relying on two‐way channels. Along the way, some fascinating benefits to high‐dimensional quantum states applied to two‐way quantum communication are also showed.
Quantum cryptography promises a paradigm shift in secure communications by leveraging the principles of quantum mechanics. This article explores mathematical frameworks central to quantum cryptographic protocols, such as linear algebra, Hilbert spaces, quantum probability, and number theory. It focuses on the theoretical underpinnings of key distribution, quantum security proofs, and error correction. The paper also highlights how mathematical tools like entropic uncertainty relations, complexity theory, and operator algebras underpin advancements in quantum cryptographic systems. These mathematical approaches ensure not only the security but also the efficiency and scalability of next-generation quantum communication networks.