Inequalities that test locality in quantum mechanics

Abstract

Quantum theory violates Bell's inequality, but not to the maximum extent that is logically possible. We derive inequalities (generalizations of Cirel'son's inequality) that quantify the upper bound of the violation, both for the standard formalism and the formalism of generalized observables (POVMs). These inequalities are quantum analogues of Bell inequalities, and they can be used to test the quantum version of locality. We discuss the nature of this kind of locality. We also go into the relation of our results to an argument by Popescu and Rohrlich (Found. Phys. 24, 379 (1994)) that there is no general connection between the existence of Cirel'son's bound and locality.

5 pages, 1 figure; the argument has been made clearer in the revised version; 1 reference added

References in corpus (4)

• Causal and localizable quantum operations
• Quadratic Bell inequalities as tests for multipartite entanglement
• Violating Bell's inequality beyond Cirel'son's bound
• Lüders Theorem for Unsharp Quantum Measurements

Cited by in corpus (10)

• Circuit Quantum Electrodynamics
• Monogamy of Correlations vs. Monogamy of Entanglement
• Proposal for generating and detecting multi-qubit GHZ states in circuit QED
• Causality and Cirel'son bounds
• Maximal CHSH violations with low efficiency photodetection and homodyne measurements
• Analysis of Bell inequality violation in superconducting qubits
• Parts and Wholes. An Inquiry into Quantum and Classical Correlations
• Bell's Inequalities, Superquantum Correlations, and String Theory
• PR-box correlations have no classical limit
• EPR Correlations Using Quaternion Spin