Performance Analysis of Multiparty GHZ-State Quantum Conference Key Agreement over Optical Fiber Channel

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 $N$-party GHZ-based QCKA system using the $N$-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 $N-1$ 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.