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BROTOCs and Quantum Information Scrambling at Finite Temperature

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Namit Anand and Paolo Zanardi

Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA

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Abstract

Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the $regularized$ finite-temperature OTOC. We introduce analytical results for the $textit{bipartite regularized}$ OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics.

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[1] Rohit Kumar Shukla, Arul Lakshminarayan, and Sunil Kumar Mishra, “Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains”, Physical Review B 105 22, 224307 (2022).

[2] Faidon Andreadakis, Namit Anand, and Paolo Zanardi, “Scrambling of Algebras in Open Quantum Systems”, arXiv:2206.02033.

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