Quantum tasks assisted by quantum noise

We introduce a notion of expected utility for quantum tasks and discuss some general conditions under which this is increased by the presence of quantum noise in the underlying resource states. We apply the resulting formalism to the specific problem of playing the parity game with ground states of the random transverse-field Ising model. This demonstrates a separation in the ground-state phase diagram between regions where rational players will be ``risk-seeking'' or ``risk-averse'', depending on whether they win the game more or less often in the presence of disorder. The boundary between these regions depends non-universally on the correlation length of the disorder. Strikingly, we find that adding zero-mean, uncorrelated disorder to the transverse fields can generate a weak quantum advantage that would not exist in the absence of noise.