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.

arXiv commentTitle changed, close to the published version

References in corpus (22)

• Quantum Games and Quantum Strategies
• Quantum strategies
• Quantum correlations with no causal order
• Quantum computations without definite causal structure
• Multi-Player Quantum Games
• Experimental realization of quantum games on a quantum computer
• Experimental Verification of an Indefinite Causal Order
• Enhanced communication with the assistance of indefinite causal order
• Three-spin interactions in optical lattices and criticality in cluster Hamiltonians
• Bell nonlocality and Bayesian game theory
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Quantum superposition of the order of parties as a communication resource
• Crossing a topological phase transition with a quantum computer
• Advantage of a quantum player over a classical one in 2x2 quantum games
• Topological order in 1D Cluster state protected by symmetry
• Measurement of the entanglement spectrum of a symmetry-protected topological state using the IBM quantum computer
• Nonlocality and conflicting interest games
• Witnesses of causal nonseparability: an introduction and a few case studies
• Quantum Game Theory Based on the Schmidt Decomposition
• Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
• Foundations of quantum theory and quantum information applications
• Quantum Chinos Game: winning strategies through quantum fluctuations