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

Quantum metrology using continuous-variable (CV) squeezed states is a powerful tool for high-precision sensing, but its performance is severely degraded by transmission loss and detection inefficiency. This paper investigates whether optical parametric amplification (OPA) can be used to make multipartite CV entangled states—specifically two-mode EPR states and four-mode cluster states—more resilient to these losses in distributed sensing applications.

The authors propose a scheme where OPA is applied to the modes of CV entangled states before performing joint balanced homodyne detection (BHD). By amplifying the phase quadrature and de-amplifying the amplitude quadrature, the OPA effectively suppresses the noise introduced by lossy channels. The study evaluates the phase estimation sensitivity using the error-propagation formula and validates the results by calculating the quantum Fisher information and the corresponding quantum Cramér-Rao bound (QCRB). They compare the performance of these entangled states against single-mode squeezed states across various loss levels, OPA gains, and displacement parameters.

The study finds that OPA-assisted sensing significantly outperforms traditional schemes in lossy environments. For the two-mode EPR state, the OPA-based approach maintains quantum enhancement even under high loss, with performance superior to individual single-mode squeezed states in specific parameter regimes. For the four-mode cluster state, the researchers demonstrate that maintaining symmetry in the loss distribution across modes is critical for achieving optimal sensitivity. Furthermore, the QCRB analysis reveals that while high OPA gain provides robustness, moderate gain settings can sometimes yield better performance depending on the specific topological structure of the entangled state.