Quantum Ziv-Zakai Bound Phase Estimation Based on Noiseless Linear Amplification in Noisy Environments

This paper explores the achievable accuracy limit for estimating unknown parameters. Within the framework of quantum Ziv-Zakai bound (QZZB), the noiseless linear amplification (NLA) technique is applied to process the initial coherent state for enhancing phase estimation performance amid photon loss and phase diffusion. The results demonstrate that increasing the NLA gain factor significantly enhances the QZZB-based phase estimation performance under bothphoton loss and phase diffusion conditions, whith particularly notable improvement in scenarios involving severe photon loss. These findings provide critical guidance for quantum information processing tasks in complex environments.