The Triangle Wave Versus the Cosine: How Classical Systems Can Optimally Approximate EPR-B Correlations

Area of Science:

• Quantum mechanics
• Foundations of physics
• Classical and quantum correlations

Background:

• Singlet correlations in composite quantum systems exhibit certainty relations and symmetries.
• Existing research often focuses on specific experimental settings and continuous rotations.

Purpose of the Study:

• To investigate classical correlation functions satisfying symmetries and certainty relations.
• To challenge the idea that quantum correlations are exclusively more extreme than classical physics allows.
• To introduce a heuristic model for classical EPR-B correlations.

Main Methods:

• Studied classical correlation functions generated by classical physical systems.
• Investigated continuous, planar rotations and binary symmetries.
• Developed a heuristic "spinning bi-coloured disk" model.
• Employed a search procedure involving random generation of classical models and Monte Carlo simulations.

Main Results:

• Identified classical EPR-B correlations that satisfy certainty relations and rotational symmetry.
• Demonstrated that imposing certainty relations and rotational symmetry allows other symmetries to be obtained "for free".
• Provided a concrete example of a classical correlation exceeding quantum correlations over a range of settings.

Conclusions:

• The widespread idea that quantum correlations are more extreme than classical physics is inaccurate.
• Classical physics can reproduce and even exceed certain quantum correlations.
• Further mathematical investigation is needed for transitions between discrete and continuous cases.