  It is known in the context of decentralised control that there exist control
strategies consistent with the requirements of a given information structure,
yet physically unimplementable through any amount of passive common randomness.
This imposes a natural set of limitations on what is achievable through common
randomness in both cooperative and competitive settings. We show that it is
possible to breach these limitations with the use of quantum-physical
architectures. In particular, we present a class of stochastic strategies that
leverage quantum entanglement to produce strategic distributions which compose
a strict superclass of strategies implemented through passive common
randomness. We investigate numerically, the `quantum advantage' offered by this
new class over a parametric family of cooperative decision problems with static
information structure. We demonstrate through variations across the parametric
family that fundamental decision theoretic elements such as information and the
cost determine the manifestation of quantum advantage in a given control
problem. Our work motivates a novel decision and control paradigm with an
enlarged space of control policies achievable by means of quantum
architectures.
