Noncommuting common causes revisited

TL;DR

This paper reexamines noncommuting common causes in quantum mechanics, refuting objections and showing they can explain correlations without triviality, thus impacting the understanding of quantum causality.

Contribution

It demonstrates that noncommuting common causes can be nontrivial, satisfy the law of total probability, and explain perfect correlations, challenging previous objections.

Findings

Noncommuting common causes can explain quantum correlations.

They can satisfy the law of total probability.

Perfect correlations can have indeterministic noncommuting common causes.

Abstract

In this paper, we revisit the concept of noncommuting common causes; refute two objections raised against them, the triviality objection and the lack of causal explanatory force; and explore how their existence modifies the EPR argument. More specifically, we show that 1) product states screening off all quantum correlations do not compromise noncommuting common causal explanations; 2) noncommuting common causes can satisfy the law of total probability; 3) perfect correlations can have indeterministic noncommuting common causes; and, as a combination of the above claims, 4) perfect correlations can have noncommuting common causes which are both nontrivial and satisfy the law of total probability.