Quantum advantage using contextual measurements of thermal 1D symmetry-protected states.

It is well known that quantum mechanics exhibits behaviors that defy local hidden variable theories. This is exemplified through nonlocal games, where separated players have to satisfy global winning conditions with limited classical communication. A quantum strategy for a nonlocal game leverages entangled resource states along with contextual measurements, demonstrating quantum advantage when it can be used to win with a probability higher than any classical strategy. The quantum advantage of the resource state is closely related to symmetry protected topological (SPT) order, a robust quantum phase of matter whose presence can be probed by string order parameters (SOPs). Previous work has shown that states in certain 1D SPT phases with sufficiently large SOPs provide quantum advantage in nonlocal games. In this work, we analyze how quantum advantage persists in a noisy situation by extending to the Gibbs state at finite temperature. Using matrix product states, we show that much of the quantum advantage holds for relevant finite system sizes, and includes physically realizable states that are promising candidates for demonstrating quantum advantage on NISQ devices.