Dynamical aspects of quantum entanglement for weakly coupled kicked tops

We investigate how the dynamical production of quantum entanglement forweakly coupled, composite quantum systems is influenced by the chaoticdynamics of the corresponding classical system, using coupled kickedtops. The linear entropy for the subsystem (a kicked top) is employed asa measure of entanglement. A perturbative formula for the entanglementproduction rate is derived. The formula contains a correlation functionthat can be evaluated only from the information of uncoupled tops. Usingthis expression and the assumption that the correlation function decaysexponentially which is plausible for chaotic tops, it is shown that {\itthe increment of the strength of chaos does not enhance the productionrate of entanglement} when the coupling is weak enough and thesubsystems (kicked tops) are strongly chaotic. The result is confirmedby numerical experiments. The perturbative approach is also applied to aweakly chaotic region, where tori and chaotic sea coexist in thecorresponding classical phase space, to reexamine a recent numericalstudy that suggests an intimate relationship between the linearstability of the corresponding classical trajectory and the entanglementproduction rate.

Refs:
A. Tanaka, H. Fujisaki, and T. Miyadera, Phys. Rev. E. 66, 045201(R) (2002);
H. Fujisaki, T. Miyadera, and A. Tanaka, Phys. Rev. E. 67, 066201 (2003);
H. Fujisaki, A. Tanaka, and T. Miyadera, J. Phys. Soc. Jpn. Suppl. C 72, 111 (2003).