Measurement- and feedback-driven adaptive dynamics in classical and quantum kicked top

In classical dynamical systems, stochastic control can guide chaotic maps onto unstable periodic orbits, creating controlled and uncontrolled phases based on the rate of control. Our previous work on classical and quantum Bernoulli maps shows that these control transitions extend to quantum dynamics, where local measurements and unitary feedback act as quantum analogs of classical control. Here, we apply these protocols to the classical and quantum kicked top, a model that spans classical, semiclassical, and quantum dynamics. We observe that control remains effective beyond the Ehrenfest timescale, where quantum interference dominates, and analytic control is lost. Moreover, we uncover hints of an entanglement transition in an effective qubit model in the quantum limit, revealing new insights into the quantum-to-classical transition. Our analysis shows that the control transition can be understood analytically, reflecting the interplay between quantization and noncommuting phase space, driven by quantum fluctuations.