Non-Hermitian sensing from the perspective of post-selected measurements

Abstract: By employing the Naimark dilation, we establish a fundamental connection between non-Hermitian quantum sensing and post-selected measurements. The sensitivity of non-Hermitian quantum sensors is determined by the effective quantum Fisher information (QFI), which incorporates the success probability of post-selection. We demonstrate that non-Hermitian sensors 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 post-selected measurements with minimal experimental trials. Our work provides a distinctive theoretical framework for investigating non-Hermitian quantum sensing and designing noise-resilient quantum metrological protocols.