OPTIMUM MEASUREMENTS FOR DISCRIMINATION AMONG SYMMETRICAL QUANTUM STATES AND PARAMETER-ESTIMATION

An optimum quantum measurement that minimizes the average probability of error is considered for symmetric quantum states. The positive oper ator-valued measure (POM) which satisfies the necessary and sufficient condition for the minimization of the average probability of error is derived by using the quantum Bayes strategy. It is also shown that th e mutual information obtained in the optimum quantum measurement becom es extremum. Furthermore, an optimum quantum measurement for parameter estimation is found for symmetric quantum states by applying the maxi mum-likelihood estimation. The optimum POM for the parameter estimatio n has the same structure as that for the quantum state discrimination.