Simulating violation of causality using a topological phase transition

We consider a topological Hamiltonian and establish correspondence between its eigenstates the resource for causal order game introduced in Ref. [1] known as process matrix. show that quantum correlations generated many-body energy of model can mimic statistics be obtained by exploiting different measurements on matrix game. This provides an interpretation expectation values observables computed states terms success probabilities As result, we ground state (GS) related to optimal strategy Subsequently, observe at point maximum violation classical bound game, corresponding undergoes second-order phase transition (QPT). The equally holds even when generalize higher number parties.