A missing causal principle: Coordination
Daniel Centeno, Antoine Coquet, Maria Ciudad Ala\~n\'on, Lucas Tendick, Marc-Olivier Renou, Elie Wolfe

TL;DR
This paper introduces the coordination principle, a causal rule for perfect coordination among parties, and demonstrates its validity in quantum theory through Bell-like inequalities and a quantum coordination task.
Contribution
It establishes a multipartite causal principle, proves its satisfaction in quantum information, and introduces a quantum coordination task involving GHZ states.
Findings
Quantum theory satisfies the coordination principle in any network.
Bell-like inequalities certify the presence of a quantum common cause.
A quantum coordination task with GHZ states requires a quantum common cause.
Abstract
We introduce the coordination principle, which states that perfect coordination, in the form of agreement on a uniformly random output, among N parties is possible only if they share a common cause. This principle is purely causal and can be viewed as a multipartite generalization of Reichenbach's common cause principle. We prove that quantum information theory satisfy the coordination principle in any network, and derive noise-tolerant Bell-like inequalities that certify the presence of a common cause. We further show that the principle is not a consequence of no-signaling and independence alone by constructing a concrete operational probabilistic theory that obeys both principles while still allowing perfect coordination without a common cause. This possibility arises only in fully general causal scenarios with intermediate transformations between preparations and measurements. We…
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