  We consider a topological Hamiltonian and establish a correspondence between
its eigenstates and the resource for a causal order game introduced in Ref. [1]
known as 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
(GS) 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, corresponding quantum many-body model
undergoes a second-order quantum phase transition (QPT). The correspondence
equally holds even when we generalize the game for a higher number of parties.
