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

Abstract

The problem of unambiguous state discrimination consists of determining which of a set of known quantum states a particular system is in. 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 has been shown to be the same as if the 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 these procedures, in particular to secret sharing, are discussed.

18 pages, two figures

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Cited by in corpus (14)

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• A framework for bounding nonlocality of state discrimination
• Distinguishability of Quantum States by Separable Operations
• Condition for unambiguous state discrimination with local operations and classical communication
• Extracting information from a qubit by multiple observers: Toward a theory of sequential state discrimination
• Entanglement Cost of Nonlocal Measurements
• Local distinguishability of orthogonal 2\otimes3 pure states
• Sequential State Discrimination and Requirement of Quantum Dissonance
• Minimum-error discrimination between a pure and a mixed two-qubit state
• Unambiguous discrimination of special sets of multipartite states using local measurements and classical communication
• Local hypothesis testing between a pure bipartite state and the white noise state
• Spatial entanglement and state engineering via four-photon Hong-Ou-Mandel interference
• Multi-partite subspaces containing no locally inaccessible information