All noncontextuality inequalities for the n-cycle scenario

Abstract

The problem of separating classical from quantum correlations is in general intractable and has been solved explicitly only in few cases. In particular, known methods cannot provide general solutions for an arbitrary number of settings. We provide the complete characterization of the classical correlations and the corresponding maximal quantum violations for the case of n >= 4 observables X_0, ...,X_{n-1}, where each consecutive pair {X_i,X_{i+1}}, sum modulo n, is jointly measurable. This generalizes both the Clauser-Horne-Shimony-Holt and the Klyachko-Can-Binicioglu-Shumovsky scenarios, which are the simplest ones for, respectively, locality and noncontextuality. In addition, we provide explicit quantum states and settings with maximal quantum violation and minimal quantum dimension.

5+3 pages, 4 figures, 11 countries. v3: Published version

References in corpus (32)

• Quantum Cryptography
• Lectures on 0/1-polytopes
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Non-locality and Communication Complexity
• A simple test for hidden variables in spin-1 system
• Bounding the set of quantum correlations
• The thermodynamic meaning of negative entropy
• Experimentally testable state-independent quantum contextuality
• The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
• State-independent experimental test of quantum contextuality
• A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality
• Testing the Hilbert space dimension
• Experimental non-classicality of an indivisible quantum system
• Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and Complementarity (PLUS AN ERRATUM)
• State-independent quantum contextuality with single photons
• Symmetries of the Bell correlation inequalities
• Computational power of correlations
• Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities
• New optimal tests of quantum nonlocality
• An entropic approach to local realism and noncontextuality
• Compatibility and noncontextuality for sequential measurements
• Entropic Inequalities and Marginal Problems
• Generalized monogamy of contextual inequalities from the no-disturbance principle
• Optimal inequalities for state-independent contextuality
• Experimental fully contextual correlations
• Hybrid ququart-encoded quantum cryptography protected by Kochen-Specker contextuality
• Entropic inequalities as a necessary and sufficient condition to noncontextuality and locality
• Coherent states, entanglement, and geometric invariant theory
• Experimental observation of impossible-to-beat quantum advantage on a hybrid photonic system
• Bell inequalities from variable elimination methods
• The extension problem for partial Boolean structures in Quantum Mechanics
• Bell inequalities as constraints on unmeasurable correlations

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• Revealing quantum contextuality using a single measurement device
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• An Effective Way of Characterizing the Quantum Nonlocality
• Experimental Quantum Advantage in the Odd-Cycle Game
• Violating the KCBS inequality with a toy mechanism
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