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

TL;DR

This paper links non-Hermitian quantum sensing to post-selected measurements, showing that their sensitivity is limited by quantum Fisher information and cannot surpass Hermitian sensors when all information is used.

Contribution

It establishes a theoretical framework connecting non-Hermitian sensing with post-selected measurements and analyzes the limits of their sensitivity based on quantum Fisher information.

Findings

Non-Hermitian sensors are bounded by the quantum Fisher information of the extended system.

The efficiency of non-Hermitian sensors can be optimized within post-selected measurement protocols.

Non-Hermitian sensors cannot outperform Hermitian sensors when all information is utilized.

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.