Unambiguous discrimination of two nonorthogonal multipartite states using local measurements and classical communication

The problem of unambiguous state discrimination consists of determining to which member of a set of known quantum states the state of a particular quantum system corresponds. We are allowed to fail to determine the state of the quantum system, but if we succeed, we are not allowed to make an error. The optimal procedure is the one with the lowest failure probability. In this dissertation, we consider a quantum system of two nonorthogonal bipartite states, |&PSgr;0⟩ and |&PSgr;1⟩. We distribute the qubits between two parties, Alice and Bob. They each perform local measurements on their qubits and then, they compare their measurement outcomes to determine which of the two possible two-particle states they have been given. We first examine the effect of restricting the classical communication between the parties, either allowing none or with some communication eliminating the possibility that one party's measurement depends on the result of the other party's. We found that in some cases the restrictions cause an increase in the failure probability, but in other cases they do not. Applications of these procedures to secret sharing are discussed. In the second part of this dissertation, we consider the cases in which, should a failure occur, both parties receive a failure signal or only one does. In the latter case, if the two states share the same Schmidt basis, the states can be discriminated with the same failure probability as would be obtained if the 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. Furthermore, we will present a scheme that demonstrates how the protocol for the case of two qubits can be experimentally realized.