Variational Limits for Phase Precision in Linear Quantum Optical Metrology

TL;DR

This paper develops universal lower bounds for phase estimation precision in noisy quantum optical systems, analyzing effects of loss, damping, and phase fluctuations, and reveals how noise impacts achievable measurement accuracy.

Contribution

It introduces a variational approach to derive analytical bounds for phase precision under various noise conditions in quantum optics.

Findings

Lower bounds for phase precision in lossy, noisy systems

Transition from Heisenberg to standard quantum limit due to photon loss

Extension of phase estimation bounds to fluctuating phases

Abstract

We apply the variational method to obtain the universal and analytical lower bounds for parameter precision in some noisy systems. We first derive a lower bound for phase precision in lossy optical interferometry at non-zero temperature. Then we consider the effect of both amplitude damping and phase diffusion on phase-shift precision. At last, we extend the constant phase estimation to the case of continuous fluctuating phase estimation, and find that due to photon losses the corresponding mean square error transits from the stochastic Heisenberg limit to the stochastic standard quantum limit as the total photon flux increases.