Quantum tasks assisted by quantum noise

TL;DR

This paper introduces a framework for evaluating quantum tasks with noise, showing that quantum disorder can sometimes enhance performance, exemplified by a parity game in a disordered quantum spin model.

Contribution

It develops a formalism for expected utility in noisy quantum tasks and demonstrates noise-induced quantum advantage in a specific spin model game.

Findings

Quantum noise can increase expected utility in certain quantum tasks.

Disorder in the transverse-field Ising model affects players' risk preferences.

Adding uncorrelated disorder can create a quantum advantage not present without noise.

Abstract

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.