Corrected Bell and non-contextuality inequalities for realistic experiments.

Area of Science:

• Quantum Information Science
• Foundations of Quantum Mechanics
• Quantum Computing

Background:

• Contextuality is a key non-classical feature of quantum correlations, vital for quantum advantage.
• It's typically defined by refuting hidden variable theories based on parameter-independence and determinism.
• Real-world experiments deviate from ideal assumptions, challenging contextuality's non-classical status and quantum advantage claims.

Purpose of the Study:

• To introduce quantifiable measures for properties underlying contextuality assumptions.
• To develop robust definitions of contextuality resilient to experimental imperfections.
• To ensure the reliability of quantum advantage derived from contextuality.

Main Methods:

• Quantification of non-signalling and measurement sharpness properties.
• Introduction of relaxed assumptions accounting for experimental deviations.
• Proof of continuity for the contextual fraction measure, demonstrating noise robustness.
• Derivation of correction terms to bound deviations from ideal contextuality.

Main Results:

• A novel definition of 'genuine contextuality' is established, robust against experimental noise and imperfections.
• The continuity of the contextual fraction is proven, ensuring its stability under realistic conditions.
• Bounds are derived showing how experimental deviations can be corrected, preserving contextuality's significance.

Conclusions:

• The developed framework provides a rigorous approach to contextuality in realistic quantum experiments.
• Genuine contextuality offers a robust foundation for quantum advantage, overcoming practical limitations.
• The findings are broadly applicable across various experimental setups and theoretical contexts in quantum information.