Classical dynamics of quantum entanglement

Abstract

We present an analysis of the entangling quantum kicked top focusing on the few qubit case and the initial condition dependence of the time-averaged entanglement SQ for spin-coherent states. We show a very strong connection between the classical phase space and the initial condition dependence of SQ even for the extreme case of two spin-1/2 qubits. This correlation is not related directly to chaos in the classical dynamics. We introduce a measure of the behavior of a classical trajectory which correlates far better with the entanglement and show that the maps of classical and quantum initial-condition dependence are both organized around the symmetry points of the Hamiltonian. We also show clear (quasi-)periodicity in entanglement as a function of number of kicks and of kick strength.

Classical-hidden-variable description for entanglement dynamics of two-qubit pure states

“…These works have shown that (i) the generation of entanglement at short times can be faithfully reproduced with the Liouville theory and (ii) pure-state entanglement, as quantified by the linear entropy of a partition, persists (actually, increases) as we move towards the classical limit ( → 0). These results were posteriorly corroborated by similar studies on different systems [20,21]. In the context of the present work, instead of figuring as a semiclassical approximation to quantum mechanics, the Liouville theory is to be interpreted as an epistemic statistical theory provided with deterministic hidden variables (trajectories), which is intended to be an alternative to quantum mechanics in describing the world.…”

“…For non-null couplings, we will generally have C cl (t) > 0, as we will see next (see Refs. [18][19][20][21] for numerical illustrations with similar quantities).…”

Impact of quantum–classical correspondence on entanglement enhancement by single-mode squeezing

“…In addition, prior squeezing of the Gaussian ensemble has the effect of increasing the number of spectral components, with a larger enhancement for the regular initial states than the chaotic counterparts just like the quantum case. Next, we plot the classical entropy of entanglement introduced by Casati et al [7] in Fig. 7.…”

Quantum tunneling effect in entanglement dynamics

“…Quantum entanglement under classical dynamics and entanglement dynamics in a two‐mode nonlinear Bosonic Hamiltonian has been studied in quantum phase space. Quantum phase space theory provides a bridge for studying the differences between quantum physics and classical physics.…”