The Bell inequality is satisfied by quantum correlations computed consistently with quantum non-commutation

TL;DR

This paper demonstrates that quantum correlations, when computed consistently with the non-commutative nature of quantum operations, satisfy Bell inequalities, challenging the traditional assumption that they are identical to commuting cases.

Contribution

The paper shows that considering the non-commutative aspects of quantum variables leads to correlations that satisfy Bell inequalities, contrary to previous assumptions.

Findings

Quantum correlations differ for commuting and non-commuting variables.

Bell inequalities are satisfied when correlations are computed with non-commutation.

The assumption that correlations are identical in both cases is invalid.

Abstract

In constructing his theorem, Bell assumed that correlation functions among non-commuting variables are the same as those among commuting variables. However, in quantum mechanics, multiple data values exist simultaneously for commuting operations while for non-commuting operations data are conditional on prior outcomes, or may be predicted as alternative outcomes of the non-commuting operations. Given these qualitative differences, there is no reason why correlation functions among non-commuting variables should be the same as those among commuting variables, as assumed by Bell. When data for commuting and noncommuting operations are predicted from quantum mechanics, their correlations are different, and they now satisfy the Bell inequality.