Graphical representation of marginal and underlying probabilities in quantum mechanics

TL;DR

This paper revisits Wigner's marginal probability theory, applying it systematically to quantum correlation measurements, deriving Bell inequalities and their corollaries like Hardy contradiction through intuitive graphical analysis.

Contribution

It introduces a graphical approach to analyze marginal and underlying probabilities in quantum mechanics, deriving new Bell inequalities and generalizations of Hardy contradiction.

Findings

Derived Bell inequalities from Wigner's theory

Established Hardy contradiction as a corollary

Provided intuitive graphical analysis for quantum correlations

Abstract

Wigner's marginal probability theory is revisited, and systematically applied to n-particle correlation measurements. A set of Bell inequalities whose corollaries are Hardy contradiction and its generalisation are derived with intuitive graphical analysis.