Operational criteria for quantum advantage in latency-constrained nonlocal games

Remote entanglement enables coordinated decision making without communication and produces correlations beyond those achievable by any classical strategy, representing a practical quantum advantage in time-critical distributed decision-making problems. However, existing analyses of quantum-classical gaps in such latency-constrained tacit coordination (LCTC) have focused on idealized models that neglect the finite stationary window of the LCTC, finite operation times, and limited entanglement generation rates, leaving fundamental constraints unaccounted for. In this work, we develop a comprehensive framework to quantitatively analyze quantum advantage in LCTC that explicitly incorporates finite-duration and finite-rate operations, as well as generalized utility structures with a limited stationary window. These advances are made possible by adapting statistical certification methods for nonlocal games to the decision-making scenarios of LCTC, identifying operational criteria that must be satisfied by the hardware implementations to realize quantum advantage with sufficient statistical significance. To meet the stringent criteria, we propose time-multiplexed, event-ready operations of cavity-assisted trapped-atom quantum network nodes that provide a continuous stream of entangled qubit pairs, with decision latencies of a microsecond and decision rates of $8\times 10^3~\text{s}^{-1}$ per channel for a representative metropolitan-scale $50$-km fiber network to keep up with the fast-changing environment, such as financial markets and electric grid networks. These results bridge the gap between the theoretical notions of the quantum-classical gap in nonlocal games and concrete implementations that meet the stringent operational criteria for achieving robust quantum advantage in realistic coordination tasks.