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This paper explores the application of quantum non-locality, a renowned andunique phenomenon acknowledged as a valuable resource. Focusing on a novelapplication, we demonstrate its quantum advantage for mobile agents engaged inspecific distributed tasks without communication. The research addresses thesignificant challenge of rendezvous on graphs and introduces a new distributedtask for mobile agents grounded in the graph domination problem. Through aninvestigation across various graph scenarios, we showcase the quantumadvantage. Additionally, we scrutinize deterministic strategies, highlightingtheir comparatively lower efficiency compared to quantum strategies. The paperconcludes with a numerical analysis, providing further insights into ourfindings.

Quantum Strategies for Rendezvous and Domination Tasks on Graphs with Mobile Agents