Playing nonlocal games with phases of quantum matter

Abstract: Nonlocal games yield an unusual perspective on entangled quantum states. The defining property of such games is that a set of players in joint possession of an entangled state can win the game with higher probability than is allowed by classical physics. This raises the following question: how far do well-known phases of quantum matter, such as the ferromagnetic phase of the quantum Ising model and the topological phase of Kitaev’s toric code Hamiltonian, provide an advantage for winning nonlocal games? We prove several new results in this setting, which can be seen as first steps towards device-independent self-testing of physically realistic ground states.