Effective quantum channel for minimum error discrimination

In this study, we consider a quantum channel that may help to discriminate quantum states, by which we may provide the solution for the unsolved problem of discrimination of quantum states. For the quantum channel to help the problem of discriminating given quantum states, the quantum channel should not change the guessing probability as well as the optimal measurement in minimum error discrimination of those quantum states. Therefore, we investigate a quantum channel that preserves an optimal measurement and the guessing probability with minimum error discrimination of quantum states. Then, we show that the channel does not exist in every set of quantum states but does exist when the channel and an optimal measurement commute with each other. The effectiveness of the channel can be shown more explicitly when the discrimination of linearly independent quantum states, which has not been solved yet, is considered. When we apply the channel to linearly independent quantum states, the discrimination of quantum states can be transformed into a problem in which the number of quantum states in discrimination is reduced, and we can provide a means of obtaining an answer to an unsolved quantum state discrimination. As an unsolved problem of discrimination of quantum states, we consider an ensemble of three pure states with real coefficients, whose subsets contain Unitary symmetry-called partial symmetry. By applying our strategy, we can provide an analytic result for optimal discrimination to the ensemble of three pure states with partial symmetry.