Continuous-variable Quantum Phase Estimation based on Machine Learning.

Making use of the general physical model of the Mach-Zehnder interferometer with photon loss which is a fundamental physical issue, we investigate the continuous-variable quantum phase estimation based on machine learning approach, and an efficient recursive Bayesian estimation algorithm for Gaussian states phase estimation has been proposed. With the proposed algorithm, the performance of the phase estimation may be improved distinguishably. For example, the physical limits (i.e., the standard quantum limit and Heisenberg limit) for the phase estimation precision may be reached in more efficient ways especially in the situation of the prior information being employed, the range for the estimated phase parameter can be extended from [0, π/2] to [0, 2π] compared with the conventional approach, and influences of the photon losses on the output parameter estimation precision may be suppressed dramatically in terms of saturating the lossy bound. In addition, the proposed algorithm can be extended to the time-variable or multi-parameter estimation framework.