Coordination Capacity for Classical-Quantum Correlations
Hosen Nator, Uzi Pereg
TL;DR
This work addresses coordinating classical and quantum correlations over networks under limited communication and common randomness. It develops a unified framework to characterize optimal tradeoffs via coordination capacity regions for a two-node network, a no-communication network, and a broadcast network, employing ensembles, random coding, and quantum resolvability. The key contributions are explicit region formulas: for the two-node setting, a region defined by $R_0\ge I(X;U)$ and $R_0+R_1\ge I(XB;U)$ (over suitable $\sigma$); for no-communication, a CR-only bound $\inf_{\sigma} I(U;ABC)$, and for broadcast, a region $R_0\ge I(X;U)$, $R_0+R_1\ge I(XB_1B_2;U)$ (over $\sigma$); with results indicating no entanglement can be generated under classical CR in these configurations. The findings generalize classical coordination results and recent quantum coordination work, offering practical guidance for quantum-enabled IoT and distributed quantum computing where links are classical but quantum resources are present. Overall, the paper advances understanding of how CR and limited communication govern the simulation of target quantum-classical correlations in multi-node networks, with potential impact on secure distributed tasks and nonlocal game strategies.
Abstract
Network coordination is considered in three basic settings, characterizing the generation of separable and classical-quantum correlations among multiple parties. First, we consider the simulation of a classical-quantum state between two nodes with rate-limited common randomness (CR) and communication. Furthermore, we study the preparation of a separable state between multiple nodes with rate-limited CR and no communication. At last, we consider a broadcast setting, where a sender and two receivers simulate a classical-quantum-quantum state using rate-limited CR and communication. We establish the optimal tradeoff between communication and CR rates in each setting.