The quantum maxima for the basic graphs of exclusivity are not reachable in Bell scenarios

Abstract

A necessary condition for the probabilities of a set of events to exhibit Bell nonlocality or Kochen-Specker contextuality is that the graph of exclusivity of the events contains induced odd cycles with five or more vertices, called odd holes, or their complements, called odd antiholes. From this perspective, events whose graph of exclusivity are odd holes or antiholes are the building blocks of contextuality. For any odd hole or antihole, any assignment of probabilities allowed by quantum mechanics can be achieved in specific contextuality scenarios. However, here we prove that, for any odd hole, the probabilities that attain the quantum maxima cannot be achieved in Bell scenarios. We also prove it for the simplest odd antiholes. This leads us to the conjecture that the quantum maxima for any of the building blocks cannot be achieved in Bell scenarios. This result sheds light on why the problem of whether a probability assignment is quantum is decidable, while whether a probability assignment within a given Bell scenario is quantum is, in general, undecidable. This also helps to undertand why identifying principles for quantum correlations is simpler when we start by identifying principles for quantum sets of probabilities defined with no reference to specific scenarios.

9 pages, 4 figures

References in corpus (21)

• Bell nonlocality
• Information Causality as a Physical Principle
• Graph-Theoretic Approach to Quantum Correlations
• A glance beyond the quantum model
• Local orthogonality as a multipartite principle for quantum correlations
• Kochen-Specker Contextuality
• Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities
• All noncontextuality inequalities for the n-cycle scenario
• Fundamental monogamy relation between contextuality and nonlocality
• Robust self-testing of quantum systems via noncontextuality inequalities
• Basic exclusivity graphs in quantum correlations
• Bell inequalities for the simplest exclusivity graph
• Synchronous observation of Bell nonlocality and state-dependent Kochen-Specker contextuality
• Quantum correlations from simple assumptions
• Almost quantum correlations violate the no-restriction hypothesis
• Multigraph approach to quantum non-locality
• Probing the limits of correlations in an indivisible quantum system
• Measurement compatibility in Bell nonlocality tests
• Testing noncontextuality inequalities that are building blocks of quantum correlations
• Quantum sets of the multicolored-graph approach to contextuality
• The problem of quantum correlations and the totalitarian principle

Cited by in corpus (1)

• Trade-off relations between Bell nonlocality and local Kochen-Specker contextuality in generalized Bell scenarios