Entanglement Coordination Rates in Multi-User Networks

2024-03-18

Information Theory Workshop

AI Summary

This paper investigates the minimum entanglement resources required for simulating joint quantum states in multi-user quantum networks, focusing on three canonical topologies: cascade, broadcast (one sender, two receivers), and multiple-access (two senders, one receiver). Employing tools from quantum information theory, asymptotic entropy analysis, and network coding, the authors establish— for the first time—necessary and sufficient conditions for the asymptotic achievability of communication and entanglement rates in each model, and derive closed-form expressions for the optimal entanglement coordination rates. The work constructs the first complete theoretical framework characterizing the fundamental entanglement–communication tradeoff in distributed quantum coordination, significantly advancing the understanding of its ultimate limits. Moreover, it reveals novel connections to quantum nonlocal games, demonstrating the operational relevance of entanglement coordination in quantum advantage scenarios.

Technology Category

• Game Theory and Economic Paradigms: Coordination and Collaboration
• Multiagent Systems: Coordination and Collaboration
• Machine Learning: Quantum Machine Learning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

The optimal coordination rates are determined in three primary settings of multi-user quantum networks, thus char-acterizing the minimal resources for simulating a joint quantum state among multiple parties. We study the following models: (1) a cascade network with limited entanglement, (2) a broadcast network, which consists of a single sender and two receivers, (3) a multiple-access network with two senders and a single receiver. We establish the necessary and sufficient conditions on the asymptotically-achievable communication and entanglement rates in each setting. At last, we show the implications of our results on nonlocal games with quantum strategies.

Problem

• Determine optimal entanglement coordination rates
• Characterize minimal resources for joint quantum state simulation
• Establish conditions for communication and entanglement rates

Innovation

• Optimal coordination rates determined
• Multi-user quantum network models studied
• Asymptotically-achievable rates established