Quantum Coordination Rates in Multi-User Networks

Quantum coordination is considered in networks with classical and quantum links. We begin with networks with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">classical links</i>, and characterize the generation of separable and classical-quantum correlations in three primary models: 1) a two-node network with limited common randomness (CR), 2) a no-communication network, and 3) a broadcast network, which consists of a single sender and two receivers. We establish the optimal tradeoff between the classical communication and CR rates in each setting, thus characterizing the minimal resources for simulating classical-quantum correlations. Next, we consider coordination in networks with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">quantum links</i>. We study the following models: 1) a cascade network with limited entanglement, 2) a broadcast network, and 3) a multiple-access network with two senders and a single receiver. We establish the optimal tradeoff between quantum communication and entanglement rates in each setting, characterizing the minimal resources for entanglement coordination. The examples demonstrate that coordination of entanglement and coordination of separable correlations behave differently. At last, we show the implications of our results on nonlocal games with quantum strategies.