Unambiguous discrimination of special sets of multipartite states using local measurements and classical communication

Abstract

We initially consider a quantum system consisting of two qubits, which can be in one of two nonorthogonal states, Ψ_0 or Ψ_1. We distribute the qubits to two parties, Alice and Bob. They each measure their qubit and then compare their measurement results to determine which state they were sent. This procedure is error-free, which implies that it must sometimes fail. In addition, no quantum memory is required; it is not necessary to store one of the qubits until the result of the measurement on the other is known. We consider the cases in which, should failure occur, both parties receive a failure signal or only one does. In the latter case, if the states share the same Schmidt basis, the states can be discriminated with the same failure probability as would be obtained if the two qubits were measured together. This scheme is sufficiently simple that it can be generalized to multipartite qubit and qudit states. Applications to quantum secret sharing are discussed. Finally, we present an optical scheme to experimenatlly realize the protocol in the case of two qubits.