Structure of Optimal State Discrimination in Generalized Probabilistic Theories

Abstract

We consider optimal state discrimination in a general convex operational framework, so-called generalized probabilistic theories (GPTs), and present a general method of optimal discrimination by applying the complementarity problem from convex optimization. The method exploits the convex geometry of states but not other detailed conditions or relations of states and effects. We also show that properties in optimal quantum state discrimination are shared in GPTs in general: i) no measurement sometimes gives optimal discrimination, and ii) optimal measurement is not unique.

arXiv comment13 pages

References in corpus (14)

• The operational meaning of min- and max-entropy
• General properties of Nonsignaling Theories
• A generalized no-broadcasting theorem
• Generalized Probability Theories: What determines the structure of quantum theory?
• Limits on non-local correlations from the structure of the local state space
• Structure of minimum-error quantum state discrimination
• Optimal State Discrimination in General Probabilistic Theories
• Measurement does not always aid state discrimination
• No-signaling Principle Can Determine Optimal Quantum State Discrimination
• Generalized quantum state discrimination problems
• Helstrom Theorem by No-Signaling Condition
• Optimality of minimum-error discrimination by the no-signalling condition
• Optimal Observables for Minimum-Error State Discrimination in General Probabilistic Theories
• Distinguishability, Ensemble Steering, and the No-Signaling Principle

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