| （英） |
In this work, we study parameter estimation about a three-parameter qubit-state model under the Bayesian setting. Recently, a tight bound for the Bayes risk is proposed, which is called the Bayesian Nagaoka-Hayashi bound. We numerically calculate the Bayesian Nagaoka-Hayashi bound by semidefinite programming for different prior distributions for the parameter space. In particular, we focus on a family of isotropic priors under the assumptions of no prefer angles known. We then compare the obtained bound with the Bayesian symmetric logarithmic derivative Cramer-Rao bound and show that the Bayesian Nagaoka-Hayashi bound is tighter.
Lastly, we show an optimal measurement and estimator that attains the Bayesian Nagaoka-Hayashi bound. |