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While classical chaos has been successfully characterized with consistenttheories and intuitive techniques, such as with the use of Lyapunov exponents,quantum chaos is still poorly understood, as well as its relation withmulti-partite entanglement and information scrambling. We consider a benchmarksystem, the kicked top model, which displays chaotic behaviour in the classicalversion, and proceed to characterize the quantum case with a thorough diagnosisof the growth of chaos and entanglement in time. As a novel tool for thecharacterization of quantum chaos, we introduce for this scope thequasi-probability distribution behind the out-of-time-ordered correlator(OTOC). We calculate the cumulative nonclassicality of this distribution, whichhas already been shown to outperform the simple use of OTOC as a probe todistinguish between integrable and nonintegrable Hamiltonians. To provide athorough comparative analysis, we contrast the behavior of the nonclassicalitywith entanglement measures, such as the tripartite mutual information of theHamiltonian as well as the entanglement entropy. We find that systems whoseinitial states would lie in the "sea of chaos" in the classical kicked-topmodel, exhibit, as they evolve in time, characteristics associated with chaoticbehavior and entanglement production in closed quantum systems. We corroboratethis indication by capturing it with this novel OTOC-based measure.

Diagnosing quantum chaos with out-of-time-ordered-correlator quasiprobability in the kicked-top model