Bayesian estimation of the wave function

Recently there have been many theoretical works on statistical inference in quantum systems. In the present Letter, we deal with the estimation of an unknown wave function under the assumption of a general parametric model. We propose the Bayesian estimation of a wave function and show the optimality result when we adopt the Bures distance as a loss function. We see some examples where the quantum state is better estimated by our method than by that based on the maximum-likelihood estimate.

► In a general parametric model of wave functions, we consider Bayesian estimation.
► Bayesian optimal estimation is better than that based point estimation.
► We obtained calculation formula of Bayesian estimator for infinite-dimensional cases.