Exclusivity principle and unphysicality of Garg-Mermin correlation
arXiv:1710.05825 · doi:10.1103/PhysRevA.98.012116
Abstract
The question concerning the physical realizability of a probability distribution is of quite importance in Quantum foundations. Specker first pointed out that this question cannot be answered from Kolmogorov's axioms alone. Lately, this observation of Specker has motivated simple principles (exclusivity principle/ local orthogonality principle) that can explain quantum limit regarding the possible sets of experimental probabilities in various nonlocality and contextuality experiments. We study Specker's observation in the simplest scenario involving three inputs each with two outputs. Then using only linear constraints imposed on joint probabilities by this principle, we reveal unphysical nature of Garg-Mermin (GM) correlation. Interestingly, GM correlation was proposed to falsify the following suggestion by Fine: if the inequalities of Clauser and Horne (CH) holds, then there exists a deterministic local hidden-variable model for a spin-1/2 correlation experiment of the Einstein-Podolsky-Rosen type, even when more than two observables are involved on each side. Our result establishes that, unlike in the CH scenario, the local orthogonality principle at single copy level is not equivalent to the no-signaling condition in the GM scenario.
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References in corpus (22)
- Bell nonlocality
- Hidden Variables and the Two Theorems of John Bell
- Information Causality as a Physical Principle
- A simple test for hidden variables in spin-1 system
- Quantum Mechanics as Quantum Measure Theory
- The uncertainty principle determines the non-locality of quantum mechanics
- Graph-Theoretic Approach to Quantum Correlations
- Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and Complementarity (PLUS AN ERRATUM)
- A glance beyond the quantum model
- Local orthogonality as a multipartite principle for quantum correlations
- A Combinatorial Approach to Nonlocality and Contextuality
- Simple explanation of the quantum violation of a fundamental inequality
- Generalized monogamy of contextual inequalities from the no-disturbance principle
- Degree of Complementarity Determines the Nonlocality in Quantum Mechanics
- Quantum Correlations are Tightly Bound by the Exclusivity Principle
- Minimal state-dependent proof of measurement contextuality for a qubit
- Bounding quantum contextuality with lack of third-order intereference
- Hardy's nonlocality argument as witness for post-quantum correlation
- Exclusivity principle and the quantum bound of the Bell inequality
- E. Specker: "The logic of non-simultaneously decidable propositions" (1960)
- Local Orthogonality provides better upper bound for Hardy's nonlocality
- Macroscopic locality with equal bias reproduces with high fidelity a quantum distribution achieving the Tsirelson's bound