Simulating violation of causality using a topological phase transition

We consider a topological Hamiltonian and establish correspondence between its eigenstates and the resource for a causal-order game introduced by Oreshkov et al. [Nat. Commun. 3, 1092 (2012), 10.1038/ncomms2076], known as the process matrix. We show that quantum correlations generated in the quantum many-body energy eigenstates of the model can mimic the statistics that can be obtained by exploiting different quantum measurements on the process matrix of the game. This provides an interpretation of the expectation values of the observables computed for the quantum many-body states in terms of the success probabilities of the game. As a result, we show that the ground state of the model can be related to the optimal strategy of the causal-order game. Subsequently, we observe that at the point of maximum violation of the classical bound in the causal-order game, the corresponding quantum many-body model undergoes a second-order quantum phase transition. The correspondence equally holds even when we generalize the game for a higher number of parties.