Linear Program for Testing Nonclassicality and an Open-Source Implementation.

Area of Science:

• Quantum Information Theory
• Foundations of Quantum Mechanics
• Computational Physics

Background:

• Demonstrating quantum phenomena that resist classical explanations is crucial for understanding quantum mechanics.
• Generalized noncontextuality provides a framework for distinguishing quantum statistics from classical models.
• Previous work has explored criteria for classical explainability in quantum experiments.

Purpose of the Study:

• To develop a computational method for testing if quantum experimental statistics violate generalized noncontextuality.
• To provide an open-source implementation for assessing classical explainability of prepare-measure experiments.
• To generalize these tests to arbitrary generalized probabilistic theories.

Main Methods:

• Formulation of the noncontextuality test as a linear program.
• Development of an open-source software tool to implement the linear program.
• Computation of minimal noise levels required for classical model existence when noncontextuality is violated.

Main Results:

• The linear program successfully determines if Born rule statistics from quantum states and effects are classically explainable.
• If not classically explainable, the method computes the minimal noise to achieve classical compliance and provides the corresponding model.
• The framework is generalized to arbitrary generalized probabilistic theories, framed as a simplex embeddability test.

Conclusions:

• The developed linear programming approach offers a robust method for detecting quantum nonclassicality.
• The open-source implementation facilitates practical testing of quantum experiments against classical models.
• The generalization to arbitrary probabilistic theories broadens the applicability of these foundational tests.