Simulating violation of causality using a topological phase transition

TL;DR

This paper demonstrates that quantum many-body energy eigenstates can simulate causal order violations in a topological model, linking quantum phase transitions to the breakdown of classical causal structures.

Contribution

It establishes a novel connection between topological quantum states, causal order games, and quantum phase transitions, providing a new interpretation of quantum correlations.

Findings

Quantum correlations mimic causal order game statistics.

Ground state relates to optimal causal order strategy.

Maximum violation coincides with a quantum phase transition.

Abstract

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.