Quantum phase estimation with local amplified 1001 state based on Wigner-function method

We demonstrate the utility of Wigner-function (WF) method in studying the quantum phase estimation. This phase estimation protocol for optical interferometry uses local amplified 1001 state as a probe state. Here, the probe state is obtained by local squeezing each mode of a single-photon-path-entangled state (1001 state). We derive analytically the WFs in describing the connection between input and output fields. In addition, the phase estimation is examined by using parity detection, and the results indicate that our strategy is super-resolving and supersensitive.