Noncontextuality inequalities for prepare-transform-measure scenarios

TL;DR

This paper introduces a systematic method to derive noncontextuality inequalities in prepare-transform-measure scenarios, enabling the certification of nonclassicality and providing tools for analyzing quantum contextuality.

Contribution

It presents a linear quantifier elimination technique to compute a polytope of correlations consistent with noncontextuality, along with algorithms and inequalities for practical certification.

Findings

Derived noncontextuality inequalities for prepare-transform-measure scenarios.

Provided a linear program to certify nonclassicality of experimental data.

Applied results to stabilizer subtheory, demonstrating violation of noncontextuality.

Abstract

We provide the first systematic technique for deriving witnesses of contextuality in prepare-transform-measure scenarios. More specifically, we show how linear quantifier elimination can be used to compute a polytope of correlations consistent with generalized noncontextuality in such scenarios. This polytope is specified as a set of noncontextuality inequalities that are necessary and sufficient conditions for observed data in the scenario to admit of a classical explanation relative to any linear operational identities, if one ignores some constraints from diagram preservation. While including these latter constraints generally leads to tighter inequalities, it seems that nonlinear quantifier elimination would be required to systematically include them. We also provide a linear program which can certify the nonclassicality of a set of numerical data arising in a prepare-transform-measure experiment. We apply our results to get a robust noncontextuality inequality for transformations that can be violated within the stabilizer subtheory. Finally, we give a simple algorithm for computing all the linear operational identities holding among a given set of states, of transformations, or of measurements.