  Quantum-classical correspondence in chaotic systems is a long-standing
problem. We describe a method to quantify Bohr's correspondence principle and
calculate the size of quantum numbers for which we can expect to observe
quantum-classical correspondence near periodic orbits of Floquet systems. Our
method shows how the stability of classical periodic orbits affects quantum
dynamics. We demonstrate our method by analyzing quantum-classical
correspondence in the quantum kicked top (QKT), which exhibits both regular and
chaotic behavior. We use our correspondence conditions to identify signatures
of classical bifurcations even in a deep quantum regime. Our method can be used
to explain the breakdown of quantum-classical correspondence in chaotic
systems.
