A shared minimum-error discrimination among three linearly dependent mirror-symmetric qubit states

We discuss how a shared minimum-error discrimination (SMD) may be implemented by two remote partners Alice and Bob. Here Bob is given a qubit prepared in one of three linearly dependent mirror-symmetric states with a priori probability. Alice has the knowledge of Bob's signal states, but Bob has not. We show that the shared generalized measurement could be realized by Alice performing a suitable unitary evolution from acting on her system to acting on Bob's system, and remotely rotating the optimal measurement directions to coincide with Bob's basis vectors. In this case, Bob could perform a local orthogonal measurement to determine his signal states with the smallest possible error and without inconclusive answers. A quantum network, which is realizable with current technology, is suggested to implement this SMD.