Lyapunov Generation of Entanglement and the Correspondence Principle

Abstract

We show how a classically vanishing interaction generates entanglement between two initially nonentangled particles, without affecting their classical dynamics. For chaotic dynamics, the rate of entanglement is shown to saturate at the Lyapunov exponent of the classical dynamics as the interaction strength increases. In the saturation regime, the one-particle Wigner function follows classical dynamics better and better as one goes deeper and deeper in the semiclassical limit. This demonstrates that quantum-classical correspondence at the microscopic level requires neither high temperatures, nor coupling to a large number of external degrees of freedom.

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• Entanglement entropy of squeezed vacua on a lattice
• Quantum ergodicity and entanglement in kicked coupled-tops
• Untangling entanglement and chaos
• Entanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength
• Non-monotonicity in the quantum-classical transition: Chaos induced by quantum effects
• Dephasing in quantum chaotic transport: a semiclassical approach
• Entanglement entropy converges to classical entropy around periodic orbits
• Quantum Corrections to Fidelity Decay in Chaotic Systems
• Classical bifurcations and entanglement in smooth Hamiltonian system
• Long-time saturation of the Loschmidt echo in quantum chaotic billiards
• Quantum-classical correspondence in entanglement production: Entropy and classical tori
• Entanglement-screening by nonlinear resonances
• Spin Squeezing, Negative Correlations, and Concurrence in the Quantum Kicked Top Model
• Entanglement transfer between bipartite systems
• Entanglement production by interaction quenches of quantum chaotic subsystems
• Statistical bounds on the dynamical production of entanglement
• Discrepancies between decoherence and the Loschmidt echo
• Correspondence principle for the diffusive dynamics of a quartic oscillator: deterministic aspects and the role of temperature
• Entanglement dynamics and classical complexity
• Out-of-Time-Order-Correlation in perturbed quantum wells