Solvable Criterion for the Contextuality of any Prepare-and-Measure Scenario

• URL: http://arxiv.org/abs/2003.06426v4
• Date: Sun, 29 May 2022 11:16:19 GMT
• Title: Solvable Criterion for the Contextuality of any Prepare-and-Measure Scenario
• Authors: Victor Gitton and Mischa P. Woods
• Abstract summary: An operationally noncontextual ontological model of the quantum statistics associated with the prepare-and-measure scenario is constructed. A mathematical criterion, called unit separability, is formulated as the relevant classicality criterion. We reformulate our results in the framework of generalized probabilistic theories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Starting from arbitrary sets of quantum states and measurements, referred to as the prepare-and-measure scenario, an operationally noncontextual ontological model of the quantum statistics associated with the prepare-and-measure scenario is constructed. The operationally noncontextual ontological model coincides with standard Spekkens noncontextual ontological models for tomographically complete scenarios, while covering the non-tomographically complete case with a new notion of a reduced space, which we motivate following the guiding principles of noncontextuality. A mathematical criterion, called unit separability, is formulated as the relevant classicality criterion -- the name is inspired by the usual notion of quantum state separability. Using this criterion, we derive a new upper bound on the cardinality of the ontic space. Then, we recast the unit separability criterion as a (possibly infinite) set of linear constraints, from which we obtain two separate hierarchies of algorithmic tests to witness the non-classicality or certify the classicality of a scenario. Finally, we reformulate our results in the framework of generalized probabilistic theories and discuss the implications for simplex-embeddability in such theories.

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