Maximal violation of tight Bell inequalities for maximal high-dimensional entanglement

Abstract

We propose a Bell inequality for high-dimensional bipartite systems obtained by binning local measurement outcomes and show that it is tight. We find a binning method for even d-dimensional measurement outcomes for which this Bell inequality is maximally violated by maximally entangled states. Furthermore, we demonstrate that the Bell inequality is applicable to continuous variable systems and yields strong violations for two-mode squeezed states.

4+ pages, 2 figures; published version

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• Bell-inequality test of spatial mode entanglement of a single massive particle
• Testing genuine multipartite nonlocality in phase space
• Testing the Clauser-Horne-Shimony-Holt inequality using observables with arbitrary spectrum
• Proposal for a macroscopic test of local realism with phase-space measurements
• Measurable criteria of generalized non-locality under the correlation symmetry
• Bell inequality for pairs of particle-number-superselection-rule restricted states
• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Continuous-variable supraquantum nonlocality
• High-dimensional Bell test for a continuous variable state in phase space and its robustness to detection inefficiency
• Noise-adaptive test of quantum correlations with quasiprobability functions