Distinguishing two-qubit states using local measurements and restricted classical communication

Abstract

The problem of unambiguous state discrimination consists of determining in which of a set of known quantum states a particular system is. One is allowed to fail but not to make a mistake. The optimal procedure is the one with the lowest failure probability. This procedure has been extended to bipartite states where the two parties Alice and Bob are allowed to manipulate their particles locally and communicate classically in order to determine which of two possible two-particle states they have been given. The failure probability of this local procedure is the same as if the two particles were together in the same location. Here we examine the effect of restricting the classical communication between the parties, either allowing none or eliminating the possibility that one party’s measurement depends on the result of the other party’s. These issues are studied for two-qubit states, and optimal procedures are found. In some cases the restrictions cause increases in the failure probability, but in other cases they do not. Applications of this procedure, in particular to secret sharing, are discussed.