Robust Entanglement-Enhanced Differential Phase Sensing

We investigate an entanglement-enhanced sensor network consisting of two nodes, each comprising an atomic ensemble, aimed at estimating the differential phase between the two ensembles while remaining insensitive to a common phase. By generating entanglement between the nodes, the sensor network can be initialized in a decoherence-free subspace with respect to the common mode, thereby achieving complete insensitivity to common-mode noise. To further enhance the protocol's robustness, we identify a two-body measurement strategy that achieves measurement variances scaling at the fundamental sensing limit. Additionally, we explore various approaches to implement the target entangled state and measurement within a cavity, considering the impact of experimental imperfections. These results provide a pathway toward robust, large-scale entangled quantum sensing in noisy environments.