Measurement compatibility in Bell nonlocality tests

Abstract

Incompatibility of observables, or measurements, is one of the key features of quantum mechanics, related, among other concepts, to Heisenberg's uncertainty relations and Bell nonlocality. In this manuscript we show, however, that even though incompatible measurements are necessary for the violation of any Bell inequality, some relevant Bell-like inequalities may be obtained if compatibility relations are assumed between the local measurements of one (or more) of the parties. Hence, compatibility of measurements is not necessarily a drawback and may, however, be useful for the detection of Bell nonlocality and device-independent certification of entanglement.

arXiv comment11 pages, 3 figures. Comments welcome!

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• Self-testing of quantum systems: a review
• Synchronous observation of Bell nonlocality and state-dependent Kochen-Specker contextuality
• Single-copy activation of Bell nonlocality via broadcasting of quantum states
• Characterization of the non-classical relation between measurement outcomes represented by non-orthogonal quantum states
• Optimal and tight Bell inequalities for state-independent contextuality sets
• Quantitative relations between different measurement contexts
• Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios
• Experimental construction of a symmetric three-qubit entangled state and its utility in testing the violation of a Bell inequality on an NMR quantum simulator
• Experimental investigation of the relation between measurement uncertainties and non-local quantum correlations
• The quantum maxima for the basic graphs of exclusivity are not reachable in Bell scenarios
• Trade-off relations between Bell nonlocality and local Kochen-Specker contextuality in generalized Bell scenarios
• A Note on Hierarchy of Quantum Measurement Incompatibilities