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arXiv:2503.21290 · Physical Review Letters

Genuine Multipartite Entanglement is Not Necessary for Standard Device-Independent Conference Key Agreement

Lewis Wooltorton, Peter J. Brown, Roger Colbeck

Published Sep 25, 2025• 1 citation
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Abstract

Conference key agreement aims to establish shared, private randomness among many separated parties in a network. Device-independent conference key agreement (DICKA) is a variant in which the source and the measurement devices used by each party need not be trusted. So far, DICKA protocols largely fall into two categories: those that rely on violating a joint Bell inequality using genuinely multipartite entangled states and those that concatenate many bipartite protocols. The question of whether a hybrid protocol exists, where a multipartite Bell inequality can be violated using only bipartite entanglement, was asked by Grasselli et al. [Quantum 7, 980 (2023)2521-327X10.22331/q-2023-04-13-980]. We answer this question affirmatively, by constructing an asymptotically secure DICKA protocol achieving the same rate as the concatenation of bipartite device-independent quantum key distribution, yet relying on a single joint Bell violation. Our results prompt further discussion on the benefits of multipartite entanglement for DICKA over its bipartite alternative, and we give an overview of different arguments for near-term devices.

DOI
10.1103/v4s8-3zl5

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Conference key agreement aims to establish shared, private randomness among many separated parties in a network. Device-independent conference key agreement (DICKA) is a variant in which the source and the measurement devices used by each party need not be trusted. So far, DICKA protocols largely fall into two categories: those that rely on violating a joint Bell inequality using genuinely multipartite entangled states and those that concatenate many bipartite protocols. The question of whether a hybrid protocol exists, where a multipartite Bell inequality can be violated using only bipartite entanglement, was asked by Grasselli et al. [Quantum 7, 980 (2023)2521-327X10.22331/q-2023-04-13-980]. We answer this question affirmatively, by constructing an asymptotically secure DICKA protocol achieving the same rate as the concatenation of bipartite device-independent quantum key distribution, yet relying on a single joint Bell violation. Our results prompt further discussion on the benefits of multipartite entanglement for DICKA over its bipartite alternative, and we give an overview of different arguments for near-term devices.
Abstract Conference key agreement (CKA), or multipartite key distribution, is a cryptographic task where more than two parties wish to establish a common secret key. A composition of bipartite quantum key distribution protocols can accomplish this task. However, the existence of multipartite quantum correlations allows for new and potentially more efficient protocols, to be applied in future quantum networks. Here, the existing quantum CKA protocols based on multipartite entanglement are reviewed, both in the device‐dependent and the device‐independent scenario.
Multipartite device-independent quantum key distribution (DI-QKD), also known as device-independent conference key agreement, enables more than two remote parties to share a common key with information-theoretic security even without trusting the devices. So far, several multipartite DI-QKD protocols have been proposed where Greenberger-Horne-Zeilinger (GHZ) states are used as multipartite entanglement. A natural question is then whether one can construct multipartite DI-QKD with the other type of multipartite entanglement. W state is of particular interest since it is intrinsically different from GHZ state and in some cases, easier to optically implement. In this paper, we show that multipartite DI-QKD is possible with W states. To this end, we construct Bell inequalities largely violated by W states, which can be used for the multipartite DI-QKD. Furthermore, we consider several different implementation scenarios. First, we analyze the minimum required detection efficiencies to extract finite amount of keys. Then we propose a long-distance multipartite DI-QKD protocol with single-photon interference and make detailed analyses with several physical implementation scenarios. We show that the protocol enables secret key distribution over longer distances than the existing multipartite DI-QKD protocols based on GHZ states. This study provides new insight about the relationship between multipartite entanglement and device-independent quantum information processing as well as opens an alternative path toward long-distance multipartite DI-QKD.
Device-independent conference key agreement (DI-CKA) enables N>2N > 2N>2 distant parties to establish a common secret key without detailed characterization of the source or measurement devices. Many existing protocols rely on full-body Bell correlators, whose measurement can be demanding for a large number of parties. Here, we show that two-body correlators alone suffice for DI-CKA using balanced Dicke states for every even N≥4N \geq 4N≥4. We construct two-body Bell inequalities and derive a tight analytical lower bound on the conditional von Neumann entropy by comparing their Bell operators with those of asymmetric Clauser-Horne-Shimony-Holt inequalities. In the ideal setting, certified key rates can approach 1−h[(N−2)/(4(N−1))]1-h[(N-2)/(4(N-1))]1−h[(N−2)/(4(N−1))], where hhh is the binary entropy function. This rate remains bounded away from zero as N→∞N \rightarrow \inftyN→∞, tending to 1−h(1/4)≈0.1891-h(1/4) \approx 0.1891−h(1/4)≈0.189 bits per key-generation round. We show that the honest implementation of our protocol is invariant under collective phase noise. Moreover, a complementary full-body Bell construction certifies positive conference-key rates from correlations arbitrarily close to the local set.
Conference key agreement allows multiple remote parties to establish a shared secret key with information-theoretical security. In device-independent conference key agreement, security can be guaranteed with minimal assumptions on the devices used, provided that a violation of a Bell inequality is observed. However, implementations are extremely challenging because high detection efficiency is required to observe loophole-free Bell violations. Here, we enhance the robustness of device-independent conference key agreement by introducing a new family of multipartite Bell inequalities called the asymmetric parity-Clauser-Horne-Shimony-Holt (CHSH) inequalities. We derive a tight analytical lower bound on the conditional von Neumann entropy of the outcomes of one of the parties in a protocol based on this inequality, including noisy preprocessing. Using this bound, we analyze robustness to detection inefficiencies as well as local and global depolarizing noise. We show that the combination of the asymmetric parity-CHSH inequality and noisy preprocessing can significantly improve the robustness to imperfections.
Device-independent conference key agreement (DI-CKA) lets a group of parties establish a shared secret key from untrusted quantum devices, with security certified by non-locality. Existing DI-CKA protocols are each built around a single Bell inequality, typically a multiparty variant of the CHSH game. DI-QKD protocols, in contrast, have been built from a much richer landscape of non-local games, and it has remained unclear how to carry this landscape over to the conference setting. We introduce $\textit{Parity-$G$ games}$, which extend any two-player game GGG to NNN players, for every NNN, provided GGG has an optimal strategy in which one player measures Pauli observables. The extension preserves the quantum and classical values of GGG, and the security of the resulting NNN-party protocol follows from an analysis of the two-player game alone. Our framework recovers the Parity-CHSH game of Ribeiro, Murta and Wehner (Phys. Rev. A, 2018) as a special case. Applied to the Mermin--Peres Magic Square Game, it yields a new NNN-player pseudo-telepathy game, the Parity Magic Square Game\textit{Parity Magic Square Game}Parity Magic Square Game, which ideal devices win in every round. We use it to construct the first\textit{first}first DI-CKA protocol based on a pseudo-telepathy game. We prove the protocol secure against coherent attacks. It produces up to two key bits per round, and at low noise its key rate exceeds that of the DI-CKA protocol based on the Parity-CHSH game.
Multipartite entanglement enables secure group key distribution among multiple users while providing immunity against hacking attacks targeting source devices, thereby realizing source-independent quantum conference key agreement (SI-QCKA). However, previous experimental demonstrations of SI-QCKA have encountered substantial technical challenges, primarily due to the low efficiency and scalability limitations inherent in the generation and distribution of multipartite entanglement. Here, we experimentally demonstrate a scalable and efficient SI-QCKA protocol using polarization-entangled photon pairs in a three-user star network, where Greenberger-Horne-Zeilinger correlations are realized via a post-matching method. We achieve a secure group key rate of 2.11×1042.11 \times 10^{4}2.11×104 bits/s under the single-user channel transmission of 1.64 ×\times× 10−110^{-1}10−1 in a symmetric channel loss network. Additionally, we conduct six sets of experiments to investigate the impact of varying channel transmission and random basis selection probabilities on secure key rates. Our work establishes an efficient pathway for SI-QCKA and demonstrates potential scalability for future large-scale multi-user quantum networks.