We propose a protocol to overcome the shot noise limit and reach the Heisenberg scaling limit for parameter estimation by using quantum optimal control and a time-reversal strategy. Exemplified through the phase estimation, which can play an important role in quantum navigation and measurement, we show that the uncertainty arising from a photon number measurement of the system can saturate the assisted Cream\'er-Rao bound, independent of the phase being estimated. In a realistic case with photon loss, we show that the optimal estimation may still be attainable by optimal control and a projective measurement on an ancilla two-level system coupled to photonic modes.
@article{arxiv.2312.14443,
title = {Time-reversal assisted quantum metrology with an optimal control},
author = {Da-Wei Luo and Ting Yu},
journal= {arXiv preprint arXiv:2312.14443},
year = {2023}
}