Quantum Coordination without Conditioning under Restricted Information

Abstract

We study which joint probability distributions can be implemented by distributed systems when agents have restricted information. Classical local operations cannot implement all distributions that are achievable with full conditioning on history. We show that shared quantum states can overcome this limitation even when using only separable states. In particular, separable states that are diagonal in a fixed basis allow certain joint distributions to be implemented through local measurements without requiring agents to condition on an inaccessible latent variable. These distributions cannot be implemented by classical local rules under the same information constraints. However, quantum implementations cannot reproduce fully adaptive dependence on past outcomes when those outcomes are observationally indistinguishable. Quantum state preparation therefore provides a partial operational substitute for perfect recall under restricted information.