Parametric Amplification of Continuous Variable Entangled State for Loss-Tolerant Quantum Distributed Sensing

Quantum metrology exploits quantum states to achieve estimation sensitivity beyond classical limits. In the continuous-variable (CV) regime, the squeezed state has been used to implement deterministic quantum sensing. However, the quantum metrology sensitivity of the squeezed state is significantly affected by losses or detection inefficiencies, which restrict its applications. In this work, quantum distributed sensing is proposed using optical parametric amplified multi-mode entanglement generated from squeezed states. It is found that the sensitivity is robust to loss or detection inefficiency with introduction of optical parametric amplification (OPA), where a two-mode Einstein-Podolsky-Rosen entangled state and a four-mode cluster state are exploited for analysis. The quantum information matrix is calculated for two-mode squeezed state to obtain the optimal bound in comparison with our scheme. It is found that with sufficient OPA gain, the overall sensitivity is robust across a wide range of loss values. This work provides a method for realizing large-scale quantum metrology in real-world applications despite losses or detection inefficiencies.