The Quantum Advantage in Binary Teams and the Coordination Dilemma: Part II

Abstract: In our previous work, we have shown that the use of a quantum architecture in decentralised control allows access to a larger space of control strategies beyond what is classically implementable through common randomness, and can lead to an improvement in the cost -- a phenomenon we called the quantum advantage. In the previous part of this two part series, we showed, however, that not all decision problems admit such an advantage. We identified a decision-theoretic property of the cost called the `coordination dilemma' as a necessary condition for the quantum advantage to manifest. In this article, we investigate the impact on the quantum advantage of a scalar parameter that captures the extent of the coordination dilemma. We show that this parameter can be bounded within an open interval for the quantum advantage to exist, and for some classes, we precisely identify this range of values. This range is found to be determined by the information of the agents.