A complete set of multidimensional Bell inequalities

Abstract

We give a multidimensional generalisation of the complete set of Bell-correlation inequalities given by Werner and Wolf, and by Zukowski and Brukner, for the two-dimensional case. Our construction applies for the n parties, two-observables case, where each observable is d-valued. The d^{d^n} inequalities obtained involve homogeneous polynomials. They define the facets of a polytope in a complex vector space of dimension d^n. We also show that these inequalities are violated by Quantum Mechanics. We exhibit examples in the three-dimensional case.

14 pages, 1 figure. Plain TeX file This version 2 adds Section 7 about violations. Section 8 (the case d=3) and bibliography have been extended accordingly

References in corpus (6)

• General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems
• Maximal violation of Clauser-Horne-Shimony-Holt inequality for two qutrits
• Multipartite Bell-type inequalities for arbitrary numbers of settings and outcomes per site
• The structure of Bell inequalities
• Measurements on Composite Qudits
• Bell inequalities, classical cryptography and fractals

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• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems
• A Quantum Key Distribution Protocol for qudits with better noise resistance
• Maximal Entanglement: Applications in Quantum Information and Particle Physics
• Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables