Coordination Requires a Common Cause in Quantum Theory

TL;DR

This paper introduces a new multipartite causal principle called the coordination principle, demonstrating its validity in quantum theory and deriving Bell-like inequalities to certify common causes.

Contribution

It proposes the coordination principle as a fundamental extension of Reichenbach's principle and proves its validity in quantum theory for four parties, with experimental certification methods.

Findings

The coordination principle does not follow from no-signaling and independence.

Quantum theory satisfies the coordination principle for four parties.

Bell-like inequalities can certify the presence of a quantum common cause.

Abstract

We propose a novel causal principle that is a genuinely multipartite extension of Reichenbach's common cause principle, namely, the coordination principle: parties in a network can achieve perfect randomized coordination--in particular, agree on a uniformly random output--only if they all share a common cause. We show that this principle does not follow from the standard no-signaling and independence principles by providing an explicit theory satisfying all these principles while violating the coordination principle. Strikingly, we prove that the coordination principle holds, however, in quantum theory for four parties, and derive noise-tolerant Bell-like inequalities that certify a common cause. We then extend these results to a genuinely quantum coordination task, showing that the four-partite GHZ state requires a quantum common cause which can also be certified by experimentally accessible Bell-like inequalities. A companion paper generalizes these results for N parties, proving that the coordination principle is satisfied in general for quantum theory.