Quantum Incompatibility Witnesses

Abstract

We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task with partial intermediate information. This is done by showing that only incompatible measurements allow for an efficient use of premeasurement information in order to improve the probability of guessing the correct state. Thus, the gap between the guessing probabilities with pre- and postmeasurement information is a witness of the incompatibility of a given collection of measurements. We prove that all linear incompatibility witnesses can be implemented as some state discrimination protocol according to this scheme. As an application, we characterize the joint measurability region of two noisy mutually unbiased bases.

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Cited by in corpus (83)

• Quantum Steering
• Quantifying quantum resources with conic programming
• All sets of incompatible measurements give an advantage in quantum state discrimination
• Incompatible measurements in quantum information science
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• Operational relevance of resource theories of quantum measurements
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• Measurement incompatibility and steering are necessary and sufficient for operational contextuality
• Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states
• Semidefinite programming relaxations for quantum correlations
• Quantum random access codes and incompatibility of measurements
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• Quantification of quantum dynamics with input-output games
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• Quantum Channel Marginal Problem
• Quantum marginal problem and incompatibility
• Distributed sampling, quantum communication witnesses, and measurement incompatibility
• Jordan products of quantum channels and their compatibility
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• Self-testing quantum states via nonmaximal violation in Hardy's test of nonlocality
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