Towards a complete cohomology invariant for non-locality and contextuality

Abstract

The sheaf theoretic description of non-locality and contextuality by Abramsky and Brandenburger sets the ground for a topological study of these peculiar features of quantum mechanics. This viewpoint has been recently developed thanks to sheaf cohomology, which provides a sufficient condition for contextuality of empirical models in quantum mechanics and beyond. Subsequently, a number of studies proposed methods to detect contextuality based on different cohomology theories. However, none of these cohomological descriptions succeeds in giving a full invariant for contextuality applicable to concrete examples. In the present work, we introduce a cohomology invariant for possibilistic and strong contextuality which is applicable to the vast majority of empirical models.

arXiv comment46 pages, 25 figures

References in corpus (5)

• Contextuality supplies the magic for quantum computation
• Contextuality in Measurement-based Quantum Computation
• The Cohomology of Non-Locality and Contextuality
• Contextuality, Cohomology and Paradox
• On the Cohomology of Contextuality

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• Contextuality as a resource for measurement-based quantum computation beyond qubits
• On Measures and Measurements: a Fibre Bundle approach to Contextuality
• Corrected Bell and Noncontextuality Inequalities for Realistic Experiments
• Cohomology and the Algebraic Structure of Contextuality in Measurement Based Quantum Computation
• Continuous-variable nonlocality and contextuality
• The Interplay between Quantum Contextuality and Wigner Negativity