Classical chaos is usually characterized by the sensitive dependence of trajectories on initial conditions. However, in quantum mechanics, the unitarity of time evolution ensures that the distances between quantum states are preserved in time. It has, therefore, been a challenge in quantum chaos to reconcile the lack of sensitive dependence on initial conditions with classical chaos. Ballentine [Fundamental Problems in Quantum Physics, edited by M. Ferrero and A. van der Merwe (Springer Netherlands, Dordrecht, 1995), pp. 15–28] has suggested a way out by constructing a parallel argument in classical mechanics based on the preservation of the inner product of phase-space densities. He has argued that the exponential separation of nearby states is a good identifier of chaos only at the level of individual trajectories. For statistical states such as quantum states and classical phase-space densities, chaos must instead be identified by some fundamentally statistical signatures. The search for these signatures is the primary goal in quantum chaos research. However, this perspective also naturally motivates the search for classical analogs of these signatures to reveal the inner machinery of chaos in quantum systems. One widely recognized signature of chaos in quantum systems is the dynamical generation of entanglement. Chaos in the classical system is correlated with a greater entanglement production in the corresponding quantum system. One of the most well-studied examples of this is the kicked top model. In this paper, we construct a classical analog of bipartite entanglement in terms of the mutual information between phase-space distributions of subsystems and find completely analogous signatures of chaos as those found in entanglement for the kicked top Hamiltonian.

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• Quantum chaos
• Quantum formalism
• Quantum foundations
• Quantum-to-classical transition