Dynamical aspects of quantum entanglement for weakly coupled kicked tops

Abstract

We investigate how the dynamical production of quantum entanglement for weakly coupled, composite quantum systems is influenced by the chaotic dynamics of the corresponding classical system, using coupled kicked tops. The linear entropy for the subsystem (a kicked top) is employed as a measure of entanglement. A perturbative formula for the entanglement production rate is derived. The formula contains a correlation function that can be evaluated only from the information of uncoupled tops. Using this expression and the assumption that the correlation function decays exponentially which is plausible for chaotic tops, it is shown that the increment of the strength of chaos does not enhance the production rate of entanglement when the coupling is weak enough and the subsystems (kicked tops) are strongly chaotic. The result is confirmed by numerical experiments. The perturbative approach is also applied to a weakly chaotic region, where tori and chaotic sea coexist in the corresponding classical phase space, to reexamine a recent numerical study that suggests an intimate relationship between the linear stability of the corresponding classical trajectory and the entanglement production rate.

Dynamical Aspects of Quantum Entanglement for Coupled Mapping Systems

“…3). To complement our previous papers, 4,5) we also discuss the wavefunction properties of the subsystems in the entanglement production region employing the Husimi representation (Sec. 4).…”

Entangling power of the quantum baker s map

“…This paper focuses, for the most part, on the first of these questions, investigating the entangling power of the Schack-Caves class of quantum baker's maps. Previous investigations of entanglement in quantized chaotic systems, for the most part, have dealt with the correlations induced by coupling two or more independent systems together [13,14,15,16,17,18,19,20,21,22]. Our approach here is quite different: each of our quantum baker's maps lives in a Hilbert space with a qubit tensor-product structure; strings of qubits form a natural basis, anchoring Hilbert space to the corresponding classical phase space, and the quantum dynamics of our baker's maps is defined explicitly in terms of this connection.…”

Scattering-induced dynamical entanglement and the quantum-classical correspondence

“…Initial work in spin-boson systems [3] and in coupled kicked tops [4] suggested that chaotic dynamics generate more and faster entanglement. This claim was subsequently revised [5,6] and efforts are now being made to derive universal relations ruling the generation of entanglement irrespective of system specifics. Different approaches based on perturbation expansions [5,7,8], Random Matrix theory [9,10] and semiclassical methods [11,12] have been proposed.…”

“…This claim was subsequently revised [5,6] and efforts are now being made to derive universal relations ruling the generation of entanglement irrespective of system specifics. Different approaches based on perturbation expansions [5,7,8], Random Matrix theory [9,10] and semiclassical methods [11,12] have been proposed. In particular it was shown and verified [11,13] that entanglement generated from initial Gaussian states averaged over configuration space depends on the global classical dynamical regime.…”

“…To quantify entanglement we will employ the linear entropy S 2 , as has been done in most previous works [3,[5][6][7][8][9][10][11][12]. Indeed for bipartite systems S 2 behaves as other measures of entanglement [20] while being convenient to compute.…”