Incompatible quantum measurements admitting a local hidden variable model

Abstract

The observation of quantum nonlocality, i.e. quantum correlations violating a Bell inequality, implies the use of incompatible local quantum measurements. Here we consider the converse question. That is, can any set of incompatible measurements be used in order to demonstrate Bell inequality violation? Our main result is to construct a local hidden variable model for an incompatible set of qubit measurements. Specifically, we show that if Alice uses this set of measurements, then for any possible shared entangled state, and any possible dichotomic measurements performed by Bob, the resulting statistics are local. This represents significant progress towards proving that measurement incompatibility does not imply Bell nonlocality in general.

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Cited by in corpus (21)

• An Invitation to Quantum Incompatibility
• Incompatible measurements in quantum information science
• Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
• A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
• Quantum measurement incompatibility does not imply Bell nonlocality
• Measurement incompatibility does not give rise to Bell violation in general
• Semidefinite programming relaxations for quantum correlations
• Quantifying Quantumness of Channels Without Entanglement
• Maximum nonlocality in the (3,2,2) scenario
• Necessary and sufficient condition for contextuality from incompatibility
• Quantum Correlations and Quantum Non-locality: a review and a few new ideas
• Device-independent tests of structures of measurement incompatibility
• Simple and maximally robust processes with no classical common-cause or direct-cause explanation
• Quantum Incompatibility of a Physical Context
• Local measurement uncertainties impose a limit on non-local quantum correlations
• Incompatibility probability of random quantum measurements
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• 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
• N term pairwise correlation inequalities, steering and joint measurability
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Theory-Independent Context Incompatibility: Quantification and Experimental Demonstration