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In this paper, we study quantum information-theoretic aspects of the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>r<\/mml:mi><mml:mi>e<\/mml:mi><mml:mi>g<\/mml:mi><mml:mi>u<\/mml:mi><mml:mi>l<\/mml:mi><mml:mi>a<\/mml:mi><mml:mi>r<\/mml:mi><mml:mi>i<\/mml:mi><mml:mi>z<\/mml:mi><mml:mi>e<\/mml:mi><mml:mi>d<\/mml:mi><\/mml:math> finite-temperature OTOC. We introduce analytical results for the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">bipartite regularized<\/mml:mtext><\/mml:mrow><\/mml:math> 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.<\/jats:p>","DOI":"10.22331\/q-2022-06-23-744","type":"journal-article","created":{"date-parts":[[2022,6,23]],"date-time":"2022-06-23T15:30:38Z","timestamp":1655998238000},"page":"744","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["BROTOCs and Quantum Information Scrambling at Finite Temperature"],"prefix":"10.22331","volume":"6","author":[{"given":"Namit","family":"Anand","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paolo","family":"Zanardi","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,6,23]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"M. 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