A Shared and Programmable Maximum-Confident Discrimination among Linearly Dependent Symmetric Qubit States

Abstract

We show how a shared and programmable maximum-confidence discrimination (SPMCD) can be implemented by two remote parters Alice and Bob. Here Bob is given a qubit prepared in one of N linearly dependent symmetric equiprobable states. Alice has the knowledge of Bob’s signal states, but Bob has not. We build a quantum network that would be able to perform various desired maximum-confidence discrimination among Bob’s measured (data) states depending on Alice’s auxiliary (program) state. The SPMCD can be thought of as a two-step process, in which a two-outcome shared and programmable probability operator measure (POM) performed on data qubit B is firstly implemented by Alice and Bob followed by a N-outcome local POM on B implemented by Bob. We explicitly construct the required POMs. The fact that the nonlocal data-program conditional evolution, which induces the shared and programmable POM, can be realized deterministically using only two partially entangled qubit pairs is notable. The successful probability of implementing this SPMCD is optimal only for one program setting. However, for a relatively large set of program settings it can be very close to the optimal value in an ordinary, local, maximum-confidence discrimination. This protocol is feasible for current experimental technology.