Resource theory of contextuality for arbitrary prepare-and-measure experiments

TL;DR

This paper develops a comprehensive resource-theoretic framework for generalized contextuality in quantum prepare-and-measure experiments, enabling quantification and analysis of contextuality as a quantum resource.

Contribution

It introduces a formal resource theory for generalized contextuality with explicit free operations and adapts resource quantifiers using linear programming methods.

Findings

Provides a linear programming characterization of contextual sets.

Defines natural monotones for generalized contextuality.

Enables quantification of contextuality in arbitrary experiments.

Abstract

Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms. Here we provide a formal resource-theoretic approach for generalized contextuality based on a physically motivated set of free operations with an explicit parametrisation. Then, using an efficient linear programming characterization for the contextual set of prepared-and-measured statistics, we adapt known resource quantifiers for contextuality and nonlocality to obtain natural monotones for generalized contextuality in arbitrary prepare-and-measure experiments.