A remark on the quantum correlation function and the Pearson coefficient of classical projections

Key Points

• This work explores the similarity between quantum correlation in singlet states and Pearson correlation in classical systems.
• Identified the quantum correlation function E(a,b) for a singlet state.
• Compared it to the Pearson correlation coefficient of two classical projections.
• Discussed connections to Fine's theorem and CHSH inequalities.
• The quantum correlation E(a,b) = −cos(a−b) matches the Pearson correlation for classical projections.
• This coincidence raises questions about potential structural significance in the foundations of quantum mechanics.