Enhancing the precision of a phase measurement through phase-sensitive non-Gaussianity

Encoding is an indispensable procedure in general phase measurement, and it is usually performed with a deterministic unitary transformation between the initial probe state and the final state. In order to improve the measurement precision, many studies focus on the optimization of the initial probe state. In this paper, we propose a scheme of subtracting one photon from the output state of an SU(1,1) interferometer. In addition to improving the output state, we find that this scheme can be used to optimize the encoding procedure. The performance of this type of optimization is only strong when the phase-sensitive negativity is induced in the Wigner function of the equivalent probe state. If a nearly perfect single-photon detector is used for the single-photon subtraction operation, the phase sensitivity within a narrow phase range can surpass 1/(?N), where N is the mean number of photons inside the SU(1,1) interferometer, and ? is the number of copies of the Gaussian probe state.