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arXiv:2605.18677

Strategy optimization for quantum conference key agreement in asymmetric star networks

Janka Memmen, Julia Kunzelmann, Nathan Walk, Jens Eisert, Julius Wallnöfer

quant-phSubmitted May 18, 2026• Announced May 19, 2026• 0 citations
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Abstract

The distribution of entangled states is a core task for quantum networks facilitating quantum communication, and the use of multipartite entangled states comes with its own set of considerations. In this work, we analyze a quantum conference agreement protocol based on GHZ states in a network with a central station to which multiple clients are connected. Using comprehensive numerical simulations, we investigate how minor variations in the scenario-such as the number of parties, the number of memories, and asymmetric distances from the central station-can drastically influence the performance of the protocol. In particular, we demonstrate that it is crucial to adjust the strategy by optimizing cutoff times. From a broader perspective, we argue that numerical simulations are an indispensable tool for protocol design for devising realistic schemes for quantum communication.

Comments
15 pages, 9 figures

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The distribution of entangled states is a core task for quantum networks facilitating quantum communication, and the use of multipartite entangled states comes with its own set of considerations. In this work, we analyze a quantum conference agreement protocol based on GHZ states in a network with a central station to which multiple clients are connected. Using comprehensive numerical simulations, we investigate how minor variations in the scenario-such as the number of parties, the number of memories, and asymmetric distances from the central station-can drastically influence the performance of the protocol. In particular, we demonstrate that it is crucial to adjust the strategy by optimizing cutoff times. From a broader perspective, we argue that numerical simulations are an indispensable tool for protocol design for devising realistic schemes for quantum communication.
Quantum conference key agreement (CKA) is useful for many applications that involve secure communication or collaboration among multiple parties. While CKA over quantum networks can be achieved using pairwise quantum key distribution, a more efficient approach is to establish keys among the parties directly through multipartite entanglement distribution. Existing studies on multipartite entanglement distribution, however, are not designed for CKA, and hence do not aim to optimize key rate. In this paper, we first develop an efficient 3-party CKA strategy based on a closed-form expression that we derive for estimating errors. We then develop a general strategy for N-party CKA that accounts for estimated key rates on individual network paths. For both cases, we use multipath routing to improve key rate. We evaluate our approach in a wide range of settings and demonstrate that it achieves high key rate and degrades gracefully when increasing the number of parties.
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.
The generation of GHZ states in quantum networks is a key element for the realization of several quantum information tasks. Given the complexity of the implementation of such generation, it is not easy to find an unambigous proof for an optimal protocol. Motivated by recent improvements in NV center manipulation, we present and compare an extensive list of protocols for generating GHZ states using realistic parameters. Furthermore, in order to establish the goodness of the various protocols, we test them on a specific application, i.e. conference key agreement. We show that for an high number of nodes the best protocol is one presented here for the first time.
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.
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.
Quantum conference key agreement (QCKA) enables the unconditional secure distribution of conference keys among multiple participants. Due to challenges in high-fidelity preparation and long-distance distribution of multi-photon entanglement, entanglement-based QCKA is facing severe limitations in both key rate and scalability. Here, we propose a source-independent QCKA scheme utilizing the post-matching method, feasible within the entangled photon pair distribution network. We introduce an equivalent distributing virtual multi-photon entanglement protocol for providing unconditional security proof even in the case of coherent attacks. For the symmetry star network, compared with the previous n -photon entanglement protocol, the conference key rate is improved from O ( η n ) to O ( η 2 ), where η is the transmittance from the entanglement source to one participant. Simulation results show that the performance of our protocol has multiple orders of magnitude advantages in the intercity distance. We anticipate that our approach will demonstrate its potential in the implementation of quantum networks.