dorsal/arxiv
View SchemaDynamical aspects of quantum entanglement for weakly coupled kicked tops
| Authors | Hiroshi Fujisaki, Takayuki Miyadera, Atushi Tanaka |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211110 |
| URL | https://arxiv.org/abs/quant-ph/0211110 |
| DOI | 10.1103/PhysRevE.67.066201 |
| Journal | Phys. Rev. E 67 (2003) 066201 |
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 {\it 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.
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"abstract": "We investigate how the dynamical production of quantum entanglement for\nweakly coupled, composite quantum systems is influenced by the chaotic dynamics\nof the corresponding classical system, using coupled kicked tops. The linear\nentropy for the subsystem (a kicked top) is employed as a measure of\nentanglement. A perturbative formula for the entanglement production rate is\nderived. The formula contains a correlation function that can be evaluated only\nfrom the information of uncoupled tops. Using this expression and the\nassumption that the correlation function decays exponentially which is\nplausible for chaotic tops, it is shown that {\\it the increment of the strength\nof chaos does not enhance the production rate of entanglement} when the\ncoupling is weak enough and the subsystems (kicked tops) are strongly chaotic.\nThe result is confirmed by numerical experiments. The perturbative approach is\nalso applied to a weakly chaotic region, where tori and chaotic sea coexist in\nthe corresponding classical phase space, to reexamine a recent numerical study\nthat suggests an intimate relationship between the linear stability of the\ncorresponding classical trajectory and the entanglement production rate.",
"arxiv_id": "quant-ph/0211110",
"authors": [
"Hiroshi Fujisaki",
"Takayuki Miyadera",
"Atushi Tanaka"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevE.67.066201",
"journal_ref": "Phys. Rev. E 67 (2003) 066201",
"title": "Dynamical aspects of quantum entanglement for weakly coupled kicked tops",
"url": "https://arxiv.org/abs/quant-ph/0211110"
},
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