Geometry of the quantum set on no-signaling faces

Abstract

Since Bell's theorem we know that quantum mechanics is incompatible with local hidden-variable models, the phenomenon known as quantum nonlocality. However, despite steady progress over the years, precise characterization of the set of quantum correlations remained elusive. There are correlations compatible with the no-signaling principle and still beyond what can be achieved within quantum theory, which has motivated the search for physical principles and computational methods to decide the quantum or postquantum behavior of correlations. Here, we identify a feature of Bell correlations that we call quantum voids: faces of the no-signaling set where all nonlocal correlations are postquantum. Considering the simplest possible Bell scenario, we give a full characterization of quantum voids, also understanding its connections to known principles and its potential use as a dimension witness.

arXiv commentClose to the published version, title modified

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• Quantum correlations on the no-signaling boundary: self-testing and more
• Device-independent bounds from Cabello's nonlocality argument
• Distilling Nonlocality in Quantum Correlations
• Observers of quantum systems cannot agree to disagree
• Nonlocality Distillation and Quantum Voids
• Geometrical self-testing of partially entangled two-qubit states
• All tight correlation Bell inequalities have quantum violations
• Information causality in multipartite scenarios
• Hardy-type paradoxes for an arbitrary symmetric bipartite Bell scenario
• Algebra of Nonlocal Boxes and the Collapse of Communication Complexity
• Comment on "Geometry of the quantum set on no-signaling faces"
• (Almost-)Quantum Bell Inequalities and Device-Independent Applications
• Analogs of absolutely maximally entangled states in nonlocal correlations via the sheaf-theoretic framework and its applications