Local unambiguous discrimination of symmetric ternary states

Abstract

We investigate unambiguous discrimination between given quantum states with a sequential measurement, which is restricted to local measurements and one-way classical communication. If the given states are binary or those each of whose individual systems is two-dimensional, then it is in some cases known whether a sequential measurement achieves a globally optimal unambiguous measurement. In contrast, for more than two states each of whose individual systems is more than two-dimensional, the problem becomes extremely complicated. This paper focuses on symmetric ternary pure states each of whose individual systems is three-dimensional, which include phase shift keyed (PSK) optical coherent states and a lifted version of "double trine" states. We provide a necessary and sufficient condition for an optimal sequential measurement to be globally optimal for the bipartite case. A sufficient condition of global optimality for multipartite states is also presented. One can easily judge whether these conditions hold for given states. Some examples are given, which demonstrate that, despite the restriction to local measurements and one-way classical communication, a sequential measurement can be globally optimal in quite a few cases.

References in corpus (28)

• Unambiguous Discrimination Between Linearly-Independent Quantum States
• Optimal local discrimination of two multipartite pure states
• Unambiguous discrimination of mixed states
• Unambiguous discrimination between quantum mixed states
• Multiple copy 2-state discrimination with individual measurements
• Reduction Theorems for Optimal Unambiguous State Discrimination of Density Matrices
• Local discrimination of mixed states
• Unambiguous State Discrimination of Coherent States with Linear Optics: Application to Quantum Cryptography
• Optimally Conclusive Discrimination of Non-orthogonal Entangled States Locally
• Minimum Decision Cost for Quantum Ensembles
• Optimal quantum detectors for unambiguous detection of mixed states
• Optimum Unambiguous Discrimination of Linearly Independent Pure States
• Revisiting the Dolinar Receiver through Multiple-Copy State Discrimination Theory
• Optimal conclusive discrimination of two states can be achieved locally
• When do Local Operations and Classical Communication Suffice for Two-Qubit State Discrimination?
• Optimal receiver for quantum cryptography with two coherent states
• Optimal Unambiguous Discrimination of Quantum States
• Multiple-copy state discrimination: Thinking globally, acting locally
• Mixed state discrimination using optimal control
• Complete solution for unambiguous discrimination of three pure states with real inner products
• Generalized quantum state discrimination problems
• The capacity of coherent-state adaptive decoders with interferometry and single-mode detectors
• Optimal sequential measurements for bi-partite state discrimination
• Structural approach to unambiguous discrimination of two mixed quantum states
• Online optimal exact identification of a quantum change point
• Optimal discrimination of optical coherent states cannot always be realized by interfering with coherent light, photon counting, and feedback
• Generalized bipartite quantum state discrimination problems with sequential measurements
• Optimal discrimination of quantum states on a two-dimensional Hilbert space by local operations and classical communication

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