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Upper Bounds on Key Rates in Device-Independent Quantum Key Distribution Based on Convex-Combination Attacks

Karol Łukanowski, Máté Farkas, Maria Balanzó-Juandó, Antonio Acín, Jan Kołodyński

Published Jan 1, 2022• 4 citations
Publisher

Abstract

We provide an efficient, generic tool for upper-bounding key rates in device-independent quantum key distribution (DIQKD) and prove that Bell nonlocality is not suf-ficient for the security of standard DIQKD protocols.
DOI
10.1364/quantum.2022.qtu4c.1

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The device-independent framework constitutes the most pragmatic approach to quantum protocols that does not put any trust in their implementations. It requires all claims, about e.g. security, to be made at the level of the final classical data in hands of the end-users. This imposes a great challenge for determining attainable key rates in device-independent quantum key distribution (DIQKD), but also opens the door for consideration of eavesdropping attacks that stem from the possibility of a given data being just generated by a malicious third-party. In this work, we explore this path and present the convex-combination attack as an efficient, easy-to-use technique for upper-bounding DIQKD key rates. It allows verifying the accuracy of lower bounds on key rates for state-of-the-art protocols, whether involving one-way or two-way communication. In particular, we demonstrate with its help that the currently predicted constraints on the robustness of DIQKD protocols to experimental imperfections, such as the finite visibility or detection efficiency, are already very close to the ultimate tolerable thresholds.
One of the main challenges in device-independent quantum key distribution (DIQKD) is achieving the required Bell violation over long distances, as the channel losses result in low overall detection efficiencies. Recent works have explored the concept of certifying nonlocal correlations over extended distances through the use of a local Bell test. Here, an additional quantum device is placed in close proximity to one party, using short-distance correlations to verify nonlocal behavior at long distances. However, existing works have either not resolved the question of DIQKD security against active attackers in this setup, or used methods that do not yield tight bounds on the key rates. In this work, we introduce a general formulation of the key rate computation task in this setup that can be combined with recently developed methods for analyzing standard DIQKD. Using this method, we show that if the short-distance devices exhibit sufficiently high detection efficiencies, positive key rates can be achieved in the long-distance branch with lower detection efficiencies as compared to standard DIQKD setups. This highlights the potential for improved performance of DIQKD over extended distances in scenarios where short-distance correlations are leveraged to validate quantum correlations.
Device-Independent Quantum Key Distribution (DIQKD) aims to generate secret keys between two parties without relying on trust in their employed devices, imposing strict noise constraints for key generation. This study explores the resilience of high-dimensional quantum systems in DIQKD, focusing on a comparison between qubits and qutrits. Lower bounds on achievable key rates are investigated through numerical optimization, while upper bounds are evaluated using the Convex-Combination attack, which has been further extended to account for arbitrary dimensions. The observed difference between these bounds provides insights into noise thresholds and potential enhancements in DIQKD scenarios, prompting debate on the merit of increased dimensions given the associated experimental efforts required.
Quantum key distribution (QKD) is a method that distributes a secret key to a sender and a receiver by the transmission of quantum particles (e.g., photons). Device-independent quantum key distribution (DIQKD) is a version of QKD with a stronger notion of security, in that the sender and receiver base their protocol only on the statistics of input and outputs of their devices as inspired by Bell's theorem. We study the rate at which DIQKD can be carried out for a given bipartite quantum state distributed between the sender and receiver or a quantum channel connecting them. We provide upper bounds on the achievable rate going beyond upper bounds possible for QKD. In particular, we construct states and channels where the QKD rate is significant while the DIQKD rate is negligible. This gap is illustrated for a practical case arising when using standard postprocessing techniques for entangled two-qubit states.
Device-independent quantum key distribution (DIQKD) is one of the most challenging tasks in quantum cryptography. The protocols and their security are based on the existence of Bell inequalities and the ability to violate them by measuring entangled states. We study the entanglement needed for DIQKD protocols in two different ways. Our first contribution is the derivation ofupper boundson the key rates of CHSH-based DIQKD protocols in terms of the violation of the inequality; this sets an upper limit on the possible DI key extraction rate from states with a given violation. Our upper bound improves on the previously known bound of Kaur et al. Our second contribution is the initiation of the study of the role ofbound entangledstates in DIQKD. We present a revised Peres conjecture stating that such states cannot be used as a resource for DIQKD. We give a first piece of evidence for the conjecture by showing that the bound entangled state found by Vertesi and Brunner, even though it can certify DI randomness, cannot be used to produce a key using protocols analogous to the well-studied CHSH-based DIQKD protocol.
Device-independent quantum key distribution (DIQKD) allows two distant parties to establish a secret key, based only on the observed Bell nonlocal distribution. It remains unclear, however, what the minimal resources for enabling DIQKD are and how to maximize the key rate from a given distribution. In the present Letter, we consider a scenario where several copies of a given quantum distribution are jointly processed via a local and classical wiring operation. We find that, under few assumptions, it is possible to activate device-independent key, that is, starting from a distribution that is useless in a DIQKD protocol, we obtain a positive asymptotic key rate by wiring several copies together. We coin this effect device-independent key activation. Our analysis focuses on the standard DIQKD protocol with one-way postprocessing, and we resort to semidefinite programming techniques for computing lower bounds on the key rate.