Entangled Rendezvous: A Possible Application of Bell Non-Locality For Mobile Agents on Networks

TL;DR

This paper explores how quantum entanglement and Bell non-locality can enhance the rendezvous problem for mobile agents on networks, providing optimal solutions and demonstrating advantages on specific graph types.

Contribution

It introduces a novel application of Bell non-locality to the rendezvous problem, offering optimal quantum and classical solutions on finite networks.

Findings

Quantum resources improve rendezvous success on cubic graphs.

Entanglement provides an advantage over classical strategies.

Optimal solutions are derived for specific network topologies.

Abstract

Rendezvous is an old problem of assuring that two or more parties, initially separated, not knowing the position of each other, and not allowed to communicate, meet without pre-agreement on the meeting point. This problem has been extensively studied in classical computer science and has vivid importance to modern applications like coordinating a fleet of drones in an enemy's territory. Quantum non-locality, like Bell inequality violation, has shown that in many cases quantum entanglement allows for improved coordination of two separated parties compared to classical sources. The non-signaling correlations in many cases even strengthened such phenomena. In this work, we analyze, how Bell non-locality can be used by asymmetric location-aware agents trying to rendezvous on a finite network with a limited number of steps. We provide the optimal solution to this problem for both agents using quantum resources, and agents with only ``classical'' computing power. Our results show that for cubic graphs and cycles it is possible to gain an advantage by allowing the agents to use assistance of entangled quantum states.