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arXiv:2405.20115 · Physical Review A

Security of device-independent quantum key distribution via monogamy relations from multipartite information causality

Lucas da Silva Pollyceno, Anubhav Chaturvedi, Chithra Raj, Pedro R. Dieguez, Marcin Pawłowski

Published Sep 8, 2025• 1 citation
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Abstract

The information causality principle $(\mathcal{IC})$ was originally proposed as a promising means to understand the extent of quantum nonlocality without invoking the full mathematical formalism of quantum theory. Beyond the foundational significance, the problem of bounding nonlocal correlations by reasonable physical principles has meaningful practical consequences, particularly for device-independent (DI) cryptographic security. In this work, we advance in this direction, demonstrating that the $\mathcal{IC}$ is enough to ensure DI security on quantum key distribution (QKD) protocols. Security is proven for a range of theoretically quantum-attainable parameters against individual attacks by a potentially postquantum eavesdropper. This result follows as a consequence of a strong form of monogamy of Bell's inequality violations, which we prove to be implied by the recently proposed multipartite formulation for $\mathcal{IC}$. Additionally, we demonstrate that the original bipartite formulation of $\mathcal{IC}$ fails to imply monogamy relations, and hence, ensure security of DIQKD, thus stressing the necessity of the multipartite framework.

DOI
10.1103/jnng-m87v

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The information causality principle (IC)(\mathcal{IC})(IC) was originally proposed as a promising means to understand the extent of quantum nonlocality without invoking the full mathematical formalism of quantum theory. Beyond the foundational significance, the problem of bounding nonlocal correlations by reasonable physical principles has meaningful practical consequences, particularly for device-independent (DI) cryptographic security. In this work, we advance in this direction, demonstrating that the IC\mathcal{IC}IC is enough to ensure DI security on quantum key distribution (QKD) protocols. Security is proven for a range of theoretically quantum-attainable parameters against individual attacks by a potentially postquantum eavesdropper. This result follows as a consequence of a strong form of monogamy of Bell's inequality violations, which we prove to be implied by the recently proposed multipartite formulation for IC\mathcal{IC}IC. Additionally, we demonstrate that the original bipartite formulation of IC\mathcal{IC}IC fails to imply monogamy relations, and hence, ensure security of DIQKD, thus stressing the necessity of the multipartite framework.
Device-independent quantum key distribution (DIQKD) represents a relaxation of the security assumptions made in usual quantum key distribution (QKD). As in usual QKD, the security of DIQKD follows from the laws of quantum physics, but contrary to usual QKD, it does not rely on any assumptions about the internal working of the quantum devices used in the protocol. In this paper, we present in detail the security proof for a DIQKD protocol introduced in Acín et al (2008 Phys. Rev. Lett. 98 230501). This proof exploits the full structure of quantum theory (as opposed to other proofs that exploit only the no-signaling principle), but only holds against collective attacks, where the eavesdropper is assumed to act on the quantum systems of the honest parties independently and identically in each round of the protocol (although she can act coherently on her systems at any time). The security of any DIQKD protocol necessarily relies on the violation of a Bell inequality. We discuss the issue of loopholes in Bell experiments in this context.
Quantum entanglement is a unique property of quantum particles. It can correlate them in such a way, that further correlations to an additional unwanted party is prevented. This renders quantum theory as the prime candidate to implement a secure distribution of an encryption key. Quantum key distribution (QKD) is dedicated to this task. A striking feature of correlations in a statistical experiment is, that they can, in principle, always be approximated. Even more so, correlations can be obtained without a detailed knowledge about the underlying physical process that generated the experimental data. This no-characterization approach is at the heart of the device-independent (DI) paradigm. Here, Bell inequalities are an imperative tool to detect nonlocal correlations, which are necessary for a DI secret key. One central subject of this thesis is multipartite DIQKD and the implications of Bell nonlocality in this context. Any DIQKD protocol involves test rounds in which the violation of a Bell inequality is checked. For multipartite DIQKD, however, not all Bell inequalities are suitable. We identify the crucial properties a Bell test requires to be a viable option. In this light, a published protocol for multipartite DIQKD is examined. We establish an incompatibility which is inherent to the proposed Bell test in combination with the required quantum states. This leads us to the conclusion, that the proposed protocol necessarily aborts. In a subsequent work, we develop a family of multipartite Bell inequalities, specifically tailored to the task of DI conference key agreement (CKA). Several features of this Bell inequality are analytically characterized. In addition, we prove its usefulness for the purposes of DICKA. To this end, semidefinite programming techniques are employed and extended to the multipartite scenario which allows us to quantify asymptotic DI conference key rates. In a second part, we explore the challenges of implementing (bipartite) long-distance DIQKD with quantum repeaters. For two repeater protocols, we describe how experimental parameters manifest themselves in DI secret-key rates. In doing so, we shed light on the fundamental differences between the usual and the DI scenario and we benchmark the threshold requirements of quantum devices to make profitable DI secret-key rates feasible. Finally, we develop a general method to describe in a non-DI setting the propagation of an important class of errors through quantum circuits in arbitrary dimensions. With this, we discuss the potential of error-corrected quantum repeaters to overcome fundamental point-to-point limitations.
ABSTRACT Quantum key distribution (QKD) is based on the laws of quantum mechanics to enable provably secure communication. Despite its theoretical security promise, practical QKD systems are vulnerable to serious attacks, including side‐channel attacks and detector loopholes, and assumes a trusted device characterisation. Device‐independent quantum key distribution (DIQKD) overcomes these limitations by relying solely on observed nonlocal correlations, certified through Bell inequality violations, thereby removing assumptions about the internal workings of the measurement devices. In this paper, we first review the foundational principles underlying DIQKD, including Bell tests and security definitions. We then examine a range of protocol designs, including CHSH‐based schemes, and non‐local game frameworks, alongside with their security proofs. We also assess recent experimental implementations and discuss source architectures, detection technologies and finite‐key analyses. Finally, we identify current open problems, such as noise tolerance, generation rates and integration with quantum networks and outline promising directions for future research to realize robust high‐performance DIQKD.
Device-independent quantum key distribution is a secure quantum cryptographic paradigm that allows two honest users to establish a secret key, while putting minimal trust in their devices. Most of the existing protocols have the following structure: first, a bipartite nonlocal quantum state is distributed between the honest users, who perform local projective measurements to establish nonlocal correlations. Then, they announce the implemented measurements and extract a secure key by postprocessing their measurement outcomes. We show that no protocol of this form allows for establishing a secret key when implemented on any correlation obtained by measuring local projective measurements on certain entangled nonlocal states, namely, on a range of entangled two-qubit Werner states. To prove this result, we introduce a technique for upper bounding the asymptotic key rate of device-independent quantum key distribution protocols, based on a simple eavesdropping attack. Our results imply that either different reconciliation techniques are needed for device-independent quantum key distribution in the large-noise regime, or Bell nonlocality is not sufficient for this task.
The Bell nonlocality is one of the most intriguing and counterintuitive phenomena displayed by quantum systems. Interestingly, such stronger-than-classical quantum correlations are somehow constrained, and one important question to the foundations of quantum theory is whether there is a physical, operational principle responsible for those constraints. One candidate is the information causality principle, which, in some particular cases, is proven to hold for quantum systems and to be violated by stronger-than-quantum correlations. In multipartite scenarios, though, it is known that the original formulation of the information causality principle fails to detect even extremal stronger-than-quantum correlations, thus suggesting that a genuinely multipartite formulation of the principle is necessary. In this work, we advance towards this goal, reporting a different formulation of the information causality principle in multipartite scenarios. By proposing a change of perspective, we obtain multipartite informational inequalities that work as necessary criteria for the principle to hold. We prove that such inequalities hold for all quantum resources and forbid some stronger-than-quantum ones. Finally, we show that our approach can be strengthened if multiple copies of the resource are available, or, counterintuitively, if noisy communication channels are employed.
Physical principles constrain the way nonlocal correlations can be distributed among distant parties. These constraints are usually expressed by monogamy relations that bound the amount of Bell inequality violation observed among a set of parties by the violation observed by a different set of parties. We prove here that much stronger monogamy relations are possible for nonsignaling correlations by showing how nonlocal correlations among a set of parties limit any form of correlations, not necessarily nonlocal, shared among other parties. In particular, we provide tight bounds between the violation of a family of Bell inequalities among an arbitrary number of parties and the knowledge an external observer can gain about outcomes of any single measurement performed by the parties. Finally, we show how the obtained monogamy relations offer an improvement over the existing protocols for device-independent quantum key distribution and randomness amplification.