Non-Hermitian-enhanced quantum sensing in an optical interferometer

In quantum metrology, measurement precision is typically bounded by the quantum Cramér-Rao bound, which relies on Hermitian observables. This paper investigates whether utilizing non-Hermitian observables for readout can enhance the sensitivity of parameter estimation beyond what is achievable with traditional Hermitian measurements, particularly in the presence of noise.

The researchers implemented a single-photon Sagnac interferometer to perform quantum parameter estimation. By encoding a parameter into the polarization state of single photons and using a non-Hermitian observable for readout, they reconstructed the complex expectation value of the observable from interference fringes. They compared the error-propagation variance of this non-Hermitian approach against the optimal Hermitian observable for the same probe state. Additionally, they tested the performance of this readout strategy under amplitude-damping noise to assess its robustness.

The experiment demonstrates that the non-Hermitian readout strategy yields a reduced error-propagation variance compared to the optimal Hermitian observable across a wide range of state parameters. Furthermore, the non-Hermitian observable shows increased robustness to amplitude-damping noise, as evidenced by a lower noise-induced variance change rate. The authors clarify that this enhancement is a result of the specific readout configuration; when the entire optical setup is analyzed as a complete positive-operator-valued measure (POVM), the results remain consistent with the standard quantum metrological limit.

This work provides an experimental framework for implementing non-Hermitian observable readout in quantum sensing. It clarifies the operational significance of non-Hermitian physics in metrology, showing that while non-Hermitian methods do not bypass fundamental quantum limits, they can effectively redistribute information to improve precision in practical, noise-prone measurement scenarios.