On coordination games with quantum correlations

Vladislav Kargin

Haozhen Situ

Şahin Kaya Özdemir, Junichi Shimamura, Fumiaki Morikoshi +1 more

Sudhakar Yarlagadda

Husein Natur, Uzi Pereg

We introduce the notion of empirical coordination for quantum correlations. Quantum mechanics enables the calculation of probabilities for experimental outcomes, emphasizing statistical averages rather than detailed descriptions of individual events. This makes empirical coordination a natural and operationally meaningful framework for quantum systems, particularly in the context of nonlocal games, which rely on repeated measurements to assess performance. We discuss how coordination performance provides new insights into the implementation and simulation of quantum nonlocal games in the empirical regime.We begin by analyzing networks with classical links, focusing on the cascade network. We establish the optimal coordination rates, which indicate the minimal resources required to simulate a quantum state on average. We then consider networks with quantum links, focusing on a broadcast setting where a single transmitter distributes entanglement between multiple receivers. Our capacity result determines the necessary and sufficient resources required for preparing correlations that can subsequently be used in quantum nonlocal games.

Husein Natur, Uzi Pereg

Coordination is a fundamental primitive in communication and information theory, in which distributed systems must collectively generate correlated behavior rather than merely exchange messages. In quantum networks, the nature of entanglement, quantum measurements, and nonclassical correlations introduces coordination possibilities unavailable classically. This article reviews recent advances in coordination over classical and quantum communication networks, focusing on empirical and strong coordination in multi-user settings. We consider the implications of coordination for nonlocal games, showing how it provides a natural framework for understanding the correlations that enable spatially separated players to improve their probability of winning. We present a unified framework for coordination using classical or quantum communication and pre-shared correlation resources. The review covers simulation of both entanglement and separable correlations across a variety of network architectures, including two-node, cascade, broadcast, and multiple-access networks. We study the operational differences between empirical and strong coordination, and the tradeoffs between communication and correlation resources, such as pre-shared randomness and entanglement. Coordination plays a major role in device-independent quantum key distribution (DI-QKD) schemes, in which parties can generate a secret key even if the devices used in the process have been prepared by an adversary. Furthermore, we examine the role of coordination in quantum repeaters, where distributed entanglement serves as a resource for long-distance quantum communication. The review highlights connections between coordination theory and applications such as distributed quantum systems, quantum internet architectures, and future communication networks.