Periodicity of dynamical signatures of chaos in quantum kicked top

A host of dynamical measures of quantum correlations -- out-of-time ordered correlators (OTOC), Loschmidt echo, generalized entanglement and observational entropy -- are useful to infer the underlying classical chaotic dynamics in quantum regime. In this work, these measures are employed to analyse quantum kicked top with kick strength $k$. It is shown that, despite the differences in their definitions, these measures are periodic with $k$, and the periodicity depends on the number of spins represented by the kicked top. The periodic behaviour arises from the structure of the kicked top Floquet operator and spans the regime in which the corresponding classical dynamics is predominantly chaotic. We also point to the reflection symmetry in Loschmidt echo and a special case of time periodicity in OTOC. This result can guide experiments towards the right choice of kick strengths to avoid repetitive dynamics.