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A tight and general finite-size security proof for Quantum Key Distribution

Thomas van Himbeeck, Peter Brown

Published Jan 13, 2024• 0 citations
OpenAlex

Abstract

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.

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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.
Despite enormous theoretical and experimental progress in quantum cryptography, the security of most current implementations of quantum key distribution is still not rigorously established. One significant problem is that the security of the final key strongly depends on the number, M, of signals exchanged between the legitimate parties. Yet, existing security proofs are often only valid asymptotically, for unrealistically large values of M. Another challenge is that most security proofs are very sensitive to small differences between the physical devices used by the protocol and the theoretical model used to describe them. Here we show that these gaps between theory and experiment can be simultaneously overcome by using a recently developed proof technique based on the uncertainty relation for smooth entropies. Although they offer significant promise, practical implementations of quantum key distribution are often not as rigorous as theory predicts. This study demonstrates how two instances of such discrepancies can be resolved by taking advantage of an enotropic formulation of the uncertainty principle.
In contrast to classical public-key cryptosystems, where the security of encoded messages relies on on computational assumptions, Quantum Key Distribution (QKD) enables two distant parties to establish a shared secret key that, when combined with a one-time pad, provides information-theoretically secure encryption, provided that the QKD protocol is supported by a rigorous security proof. In the last decades, security proofs robust against a wide range of eavesdropping strategies have established the theoretical soundness of several QKD protocols. However, most proofs are based on idealized models of the physical systems involved in such protocols and often include assumptions that are not satisfied in practical implementations. This mismatch creates a gap between theoretical security guarantees and actual experimental realizations, making QKD protocols vulnerable to attacks. To ensure the security of real-world QKD systems, it is therefore essential to account for imperfections in security analyses. In this article, we present an overview of recent analytical and numerical developments in QKD security proofs, which provide a versatile approach for incorporating imperfections and re-establishing the security of quantum communication protocols under realistic conditions.
Quantum cryptographic protocols solve the longstanding problem of distributing a shared secret string to two distant users by typically making use of one-way quantum channel. However, alternative protocols exploiting two-way quantum channel have been proposed for the same goal and with potential advantages. Here, we overview a security proof for two-way quantum key distribution protocols, against the most general eavesdropping attack, that utilize an entropic uncertainty relation. Then, by resorting to the “smooth” version of involved entropies, we extend such a proof to the case of finite key size. The results will be compared to those available for one-way protocols showing some advantages.
Since they were first introduced, quantum communications have evolved into a mature technology that is making its way to market. Quantum key distribution (QKD), in particular, allows the exchange of information with security that stems from the very laws of quantum mechanics and hence is not impaired by future technological advances. These same laws, however, restrict the QKD transmission range, as they forbid a straightforward amplification of quantum signals. This leads to a fundamental rate-distance bound known as the “repeaterless secret key capacity” (SKC0), which was thought to be impossible to overcome without a full-fledged quantum repeater. The recent proposal of “Twin-Field QKD” challenged this belief and showed how to overcome the SKC0 with an effective quantum repeater, realisable with present-day technology. This allows to perform QKD over long-distance and high-loss channels. In my talk, I will review the main concepts and most significant results behind this novel idea.
Distributed-phase-reference quantum key distribution stands out for its easy implementation with present day technology. For many years, a full security proof of these schemes in a realistic setting has been elusive. We solve this long-standing problem and present a generic method to prove the security of such protocols against general attacks. To illustrate our result, we provide lower bounds on the key generation rate of a variant of the coherent-one-way quantum key distribution protocol. In contrast to standard predictions, it appears to scale quadratically with the system transmittance.