Non-Hermitian sensing from the perspective of postselected measurements

By employing the Naimark dilation, we establish a fundamental connection between non-Hermitian quantum sensing and postselected measurements. The sensitivity of non-Hermitian quantum sensors is determined by the effective quantum Fisher information (QFI), which incorporates the success probability of postselection. We demonstrate that non-Hermitian sensors, regardless of the specific form of decoherence or the choice of probe states, cannot outperform their Hermitian counterpart when all information is harnessed, since the total QFI for the extended system constrains the effective QFI of the non-Hermitian subsystem. Moreover, we quantify the efficiency of non-Hermitian sensors with the ratio of the effective QFI to the total QFI, which can be optimized within the framework of postselected measurements with minimal experimental trials. In addition, the performances of non-Hermitian sensors versus different types of technical noises can be judged using our framework. Our work provides a distinctive theoretical framework for investigating non-Hermitian quantum sensing and designing noise-resilient quantum metrological protocols.