Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality

Abstract

We investigate the relation between the incompatibility of quantum measurements and quantum nonlocality. We show that any set of measurements that is not jointly measurable (i.e. incompatible) can be used for demonstrating EPR steering, a form of quantum nonlocality. This implies that EPR steering and (non) joint measurability can be viewed as equivalent. Moreover, we discuss the connection between Bell nonlocality and joint measurability, and give evidence that both notions are inequivalent. Specifically, we exhibit a set of incompatible quantum measurements and show that it does not violate a large class of Bell inequalities. This suggest the existence of incompatible quantum measurements which are Bell local, similarly to certain entangled states which admit a local hidden variable model.

7 pages, 1 figure, 2 tables. Typos corrected, more details on the SDP in appendix C

References in corpus (6)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• One-way Einstein-Podolsky-Rosen Steering
• Joint measurability of generalized measurements implies classicality
• Notes on Joint Measurability of Quantum Observables
• All quantum states useful for teleportation are nonlocal resources

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• Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states
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• On the origin of nonclassicality in single systems
• Characterizing quantum correlations in the nonsignaling framework
• The complexity of compatible measurements
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Measurement incompatibility vs. Bell non-locality: an approach via tensor norms
• Analysis of Quantum Steering Measures
• Detecting Tripartite Steering via Quantum Entanglement
• N term pairwise correlation inequalities, steering and joint measurability
• Recovering quantum entanglement after its certification
• Maximal violation of steering inequalities and the matrix cube
• Joint-measurability and quantum communication with untrusted devices
• Quantum observable's reality erasure with spacelike-separated operations
• Class of Bell-Clauser-Horne inequalities for testing quantum nonlocality
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• Naimark dilations of qubit POVMs and joint measurements
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Revealing the quantitative relation between simultaneous correlations in complementary bases and quantum steering for two-qubit Bell diagonal states
• "All-versus-nothing" proof of genuine tripartite steering and entanglement certification in the two-sided device-independent scenario
• Averaged fidelity-based steering criteria
• Necessary and Sufficient Condition for Randomness Certification from Incompatibility
• Postquantum steering
• Experimentally determining the incompatibility of two qubit measurements
• Diagnosing steerability of a bipartite state with the nonsteering threshold
• Physical interpretation of nonlocal quantum correlation through local description of subsystems
• Cost of Simulating Entanglement in Steering Scenario
• A Fisher information-based incompatibility criterion for quantum channels
• Relating CP divisibility of dynamical maps with compatibility of channels
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• Compressing continuous variable quantum measurements
• Measurement-device-independent measure of steerability and witnesses for all steerable resources
• Entanglement Cost for Steering Assemblages
• Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables
• A Note on Hierarchy of Quantum Measurement Incompatibilities
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