A nearly optimal and robust protocol for nonlinear phase estimation using coherent states

Jian-Dong Zhang, Zi-Jing Zhang, Jun-Yan Hu, Long-Zhu Cen, Yi-Fei Sun, Chen-Fei Jin, Yuan Zhao

Published 2019-06-21Version 1

We propose a protocol for the second-order nonlinear phase estimation with a coherent state as input and balanced homodyne detection as measurement strategy. The sensitivity is sub-Heisenberg limit, which scales as $N^{-3/2}$ for $N$ photons on average. By ruling out hidden resources in quantum Fisher information, the fundamental sensitivity limit is recalculated and compared to the optimal sensitivity of our protocol. In addition, we investigate the effect of photon loss on sensitivity, and discuss the robustness of measurement strategy. The results indicate that our protocol is nearly optimal and robust.