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arXiv:2207.01643 · npj Quantum Information

Conference key agreement in a quantum network

Alexander Pickston, Joseph Ho, Andrés Ulibarrena, Federico Grasselli, Massimiliano Proietti, Christopher L. Morrison, Peter Barrow, Francesco Graffitti, Alessandro Fedrizzi

Published Aug 22, 2023• 53 citations
arXivHTMLPDF

Abstract

Abstract Quantum conference key agreement (QCKA) allows multiple users to establish a secure key from a shared multi-partite entangled state. In a quantum network, this protocol can be efficiently implemented using a single copy of a N-qubit Greenberger-Horne-Zeilinger (GHZ) state to distil a secure N-user conference key bit, whereas up to N-1 entanglement pairs are consumed in the traditional pair-wise protocol. We demonstrate the advantage provided by GHZ states in a testbed consisting of a photonic six-user quantum network, where four users can distil either a GHZ state or the required number of Bell pairs for QCKA using network routing techniques. In the asymptotic limit, we report a more than two-fold enhancement of the conference key rate when comparing the two protocols. We extrapolate our data set to show that the resource advantage for the GHZ protocol persists when taking into account finite-key effects.

DOI
10.1038/s41534-023-00750-4

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Abstract Quantum conference key agreement (QCKA) allows multiple users to establish a secure key from a shared multi-partite entangled state. In a quantum network, this protocol can be efficiently implemented using a single copy of a N-qubit Greenberger-Horne-Zeilinger (GHZ) state to distil a secure N-user conference key bit, whereas up to N-1 entanglement pairs are consumed in the traditional pair-wise protocol. We demonstrate the advantage provided by GHZ states in a testbed consisting of a photonic six-user quantum network, where four users can distil either a GHZ state or the required number of Bell pairs for QCKA using network routing techniques. In the asymptotic limit, we report a more than two-fold enhancement of the conference key rate when comparing the two protocols. We extrapolate our data set to show that the resource advantage for the GHZ protocol persists when taking into account finite-key effects.
Abstract Multi-party quantum key sharing is the foundation for constructing quantum communication networks. The source-independent quantum conference key agreement (QCKA) distributes multiple Bell state pairs, which are post-processed to construct equivalent Greenberger-Horne-Zeilinger (GHZ) states and achieve multi-party key sharing. This helps maintain key rates at reasonable levels as the number of users increases, improving practicality and scalability. However, in the original source-independent QCKA protocol, the users receiving Bell states are assumed to be symmetrically distributed, which actually contradicts the distinct functional roles of the protocol participants (Alice and Bobs), and also limits the conference key rate of the protocol. To address this, we propose a source-independent QCKA protocol under an asymmetric architecture and perform simulations using parameters from existing commercial products, increasing the conference key rate and reducing deployment costs in practical applications.
Quantum conference key agreement (QCKA) enables multiple spatially separated users to establish a common key with composable information-theoretic security by exploiting multipartite quantum correlations. Greenberger--Horne--Zeilinger (GHZ) states are a natural resource for this task, but their distribution over optical fiber is degraded by transmission loss, polarization decoherence, and detector imperfections. We investigate the finite-key performance of an NNN-party GHZ-based QCKA system using the NNN-BB84 protocol, where each optical link is modeled by extending the bipartite erasure--Pauli channel to incorporate detector dark counts. We characterize the impact of this quantum channel on the shared GHZ state and derive closed-form expressions for the error rates. The analytical results reveal that the local bit-error rate depends only on transmissivity and dark counts, while the global phase-error rate compounds over all N−1N-1N−1 links and therefore degrades faster with both distance and the number of parties. These error rates are integrated into a finite-key secret-key-rate (SKR) framework, in which we optimize the parameter-estimation probability via Brent's derivative-free method. Numerical results show that increasing fiber distance and network size reduce the achievable SKR. Furthermore, the optimized parameter-estimation probability consistently increases the SKR and extends the maximum secure distance relative to a fixed-allocation baseline, with comparison to the asymptotic limit quantifying the residual finite-key penalty.
Anonymous quantum conference key agreement (AQCKA) allows a group of users within a network to establish a shared cryptographic key without revealing their participation. Although this can be achieved using bipartite primitives alone, it is costly in the number of network rounds required. By allowing the use of multi-partite entanglement, there is a substantial efficiency improvement. We experimentally implement the AQCKA task in a six-user quantum network using Greenberger–Horne–Zeilinger (GHZ)-state entanglement and obtain a significant resource cost reduction in line with theory when compared to a bipartite-only approach. We also demonstrate that the protocol retains an advantage in a four-user scenario with finite key effects taken into account.
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.
Quantum networks aim to enable quantum information tasks among multiple parties. Quantum conference key agreement (QCKA) is a typical task in quantum networks, which distributes information-theoretically secure keys among multiple users. However, QCKA relying on directly distributing Greenberger-Horne-Zeilinger (GHZ) states over long distances faces significant challenges due to the fragility of these states. Measurement-device-independent QCKA (MDI-QCKA) based on distributing the postselected GHZ entanglement can address this issue and eliminate all loopholes in detection side channels. Here, by developing three-photon GHZ interference technology with high visibility among three independent coherent sources, we realized the first MDI-QCKA experiment over a 60 km fiber link, achieving a secret key rate of 45.5 bits/s. Our result represents a significant step towards practical long-distance QCKA using realistic devices. Moreover, the technology we developed opens the way to future multiparty quantum communications in quantum networks.
Quantum conference key agreement (QCKA) enables multiple users to establish a common secret key with information-theoretic security and is regarded as a key primitive for secure communication in future quantum networks. However, practical implementations of QCKA typically suffer from higher noise levels than conventional bipartite quantum key distribution (QKD), making the improvement of the tolerable error threshold an important challenge. Gottesman and Lo proposed two preprocessing procedures for QKD with two-way classical communication, known as the B-step and the P-step, which enhance the tolerable error threshold. In this paper, we analyze the asymptotic security of QCKA with tripartite GHZ states and two measurement bases using two-way classical communication, including multiple B-steps and P-steps. We derive the corresponding secure key rate analytically and demonstrate that iterative B-steps can increase the tolerable error threshold beyond 20%, significantly improving upon the approximately 11% threshold achievable without two-way classical communication and the approximately 15% threshold obtained with only a single B-step. Our results show that two-way classical communication can substantially enhance the robustness of practical QCKA protocols.