Simulating violation of causality using a topological 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.

Title changed, close to the published version

References in corpus (5)

• Experimental Verification of an Indefinite Causal Order
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Nonlocality and conflicting interest games
• Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
• Foundations of quantum theory and quantum information applications