Geometric coherence and quantum state discrimination

Abstract

The operational meaning of coherence measure lies at very heart of the coherence theory. In this paper, we provide an operational interpretation for geometric coherence, by proving that the geometric coherence of a quantum state is equal to the minimum error probability to discriminate a set of pure states with von Neumann measurement. On the other hand, we also show that a task to ambiguously discriminate a set of linearly independent pure states can be also regards as a problem of calculating geometric coherence. That is, we reveal an equivalence relation between ambiguous quantum state discrimination and geometric coherence. Based on this equivalence, moreover, we improve the upper bound for geometric coherence and give the explicit expression of geometric coherence for a class of states. Besides, we establish a complementarity relation of geometric coherence and path distinguishability, with which the relationship between $l_1$-norm of coherence and geometric coherence is obtained. Finally, with geometric coherence, we study multiple copies quantum state discrimination and give an example to show how to discriminate two pure states.

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Cited by in corpus (13)

• Resource theory of coherence based on positive-operator-valued measures
• Partial coherence and quantum correlation with fidelity and affinity distances
• Average skew information-based coherence and its typicality for random quantum states
• Estimating quantum coherence by noncommutativity of any observable and its incoherent part
• Discriminating bipartite mixed states by local operations
• Trade-off relations of geometric coherence
• All multipartite entanglements are quantum coherences in locally distinguishable bases
• Unambiguous state discrimination with intrinsic coherence
• Correlation between resource-generating capacities of quantum gates
• Discrimination of Coherent States via Atom-Field Interaction without Rotation Wave Approximation
• Maximal intrinsic randomness of a quantum state
• Quantum partial coherence measures constructed from Fisher information
• Trace-distance-based complementarity relations in a multipath interferometer