Contextual advantages and certification for maximum confidence discrimination

Abstract

One of the most fundamental results in quantum information theory is that no measurement can perfectly discriminate between non-orthogonal quantum states. In this work, we investigate quantum advantages for discrimination tasks over noncontextual theories by considering a maximum confidence measurement that unifies different strategies of quantum state discrimination, including minimum-error and unambiguous discrimination. We first show that maximum confidence discrimination, as well as unambiguous discrimination, contains contextual advantages. We then consider a semi-device independent scenario of certifying maximum confidence measurement. The scenario naturally contains undetected events, making it a natural setting to explore maximum confidence measurements. We show that the certified maximum confidence in quantum theory also contains contextual advantages. Our results establish how the advantages of quantum theory over a classical model may appear in a realistic scenario of a discrimination task.

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Cited by in corpus (29)

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• Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
• A linear program for testing nonclassicality and an open-source implementation
• Contextuality with vanishing coherence and maximal robustness to dephasing
• Maximum confidence measurement for qubit states
• Prepare-and-measure scenarios with photon-number constraints
• Contextuality in anomalous heat flow
• Alternative robust ways of witnessing nonclassicality in the simplest scenario
• Self-testing of multiple unsharpness parameters through sequential violations of non-contextual inequality
• Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs
• Contextuality witness inspired by optimal state discrimination
• Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks
• Connecting XOR and XOR* games
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• Global restrictions under local state discrimination
• Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities
• Entanglement witness and nonlocality in confidence of measurement from multipartite quantum state discrimination
• Discrimination and certification of unknown quantum measurements
• Contextual advantages across two-state discrimination strategies
• Failure of epistemic models to explain the antidistinguishability of quantum mixed preparations
• Contextuality-enhanced quantum state discrimination under fixed failure probability
• Effects of underlying topology on quantum state discrimination
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory
• Typicality of Contextuality
• Operational Coherent Measurements with Steering and Randomness