Quantum entanglement and its classical analogue - classical separability - will be treated in a dynamical system consisting of two coupled perturbed cat maps. The dynamics of the classical system will be observed through time evolution of the probability density on the classical phase space. To study the quantum-classical correspondence the classical dynamical system is quantized and the stemming quantum dynamics are presented as time-evolving quasi-probabilities on the classical phase space via Wigner functions. To reach optimal quantum-classical correspondence the initial state on phase space is equal to Wigner function of a coherent state. For phase space functions, specifically for classical probability density and Wigner function, we introduce separability entropy, which is in the case of a Wigner function related simply to quantum entanglement entropy. The results will be presented as the similarities and the differences between time-evolved separability entropies of a classical and quantum systems under variable dynamical parameters.
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