  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 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.
