A linear program for testing nonclassicality and an open-source implementation

TL;DR

This paper introduces a linear programming method and open-source tool to test whether quantum experiment statistics can be explained by classical noncontextual models, applicable to quantum and generalized probabilistic theories.

Contribution

It formulates a linear program for testing nonclassicality and provides an open-source implementation, extending the analysis to generalized probabilistic theories.

Findings

The program determines if quantum statistics are classically explainable.

It computes minimal noise needed for classical explanation when not initially explainable.

The method generalizes to arbitrary generalized probabilistic theories.

Abstract

A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an open-source implementation of it which tests whether or not any given prepare-measure experiment is classically-explainable in this sense. The input to the program is simply an arbitrary set of quantum states and an arbitrary set of quantum effects; the program then determines if the Born rule statistics generated by all pairs of these can be explained by a classical (noncontextual) model. If a classical model exists, it provides an explicit model. If it does not, then it computes the minimal amount of noise that must be added such that a model does exist, and then provides this model. We generalize all these results to arbitrary generalized probabilistic theories (and accessible fragments thereof) as well; indeed, our linear program is a test of simplex-embeddability.