dorsal/arxiv
View SchemaQuantum Entanglement dependence on bifurcations and scars in non autonomous systems. The case of Quantum Kicked Top
| Authors | George Stamatiou, Demetris P. K. Ghikas |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0702172 |
| URL | https://arxiv.org/abs/quant-ph/0702172 |
| DOI | 10.1016/j.physleta.2007.04.003 |
Abstract
Properties related to entanglement in quantum systems, are known to be associated with distinct properties of the corresponding classical systems, as for example stability, integrability and chaos. This means that the detailed topology, both local and global, of the classical phase space may reveal, or influence, the entangling power of the quantum system. As it has been shown in the literature, the bifurcation points, in autonomous dynamical systems, play a crucial role for the onset of entanglement. Similarly, the existence of scars among the quantum states seems to be a factor in the dynamics of entanglement. Here we study these issues for a non-autonomous system, the Quantum Kicked Top, as a collective model of a multi-qubit system. Using the bifurcation diagram of the corresponding classical limit (the Classical Kicked Top), we analyzed the pair-wise and the bi-partite entanglement of the qubits and their relation to scars, as a function of the critical parameter of the system. We found that the pair-wise entanglement and pair-wise negativity show a strong maximum precisely at the bifurcation points, while the bi-partite entanglement changes slope at these points. We have also investigated the connection between entanglement and the fixed points on the branch of the bifurcation diagram between the two first bifurcation points and we found that the entanglement measures take their extreme values precisely on these points. We conjecture that our results on this behaviour of entanglement is generic for many quantum systems with a non-linear classical analogue.
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"abstract": "Properties related to entanglement in quantum systems, are known to be\nassociated with distinct properties of the corresponding classical systems, as\nfor example stability, integrability and chaos. This means that the detailed\ntopology, both local and global, of the classical phase space may reveal, or\ninfluence, the entangling power of the quantum system. As it has been shown in\nthe literature, the bifurcation points, in autonomous dynamical systems, play a\ncrucial role for the onset of entanglement. Similarly, the existence of scars\namong the quantum states seems to be a factor in the dynamics of entanglement.\nHere we study these issues for a non-autonomous system, the Quantum Kicked Top,\nas a collective model of a multi-qubit system. Using the bifurcation diagram of\nthe corresponding classical limit (the Classical Kicked Top), we analyzed the\npair-wise and the bi-partite entanglement of the qubits and their relation to\nscars, as a function of the critical parameter of the system. We found that the\npair-wise entanglement and pair-wise negativity show a strong maximum precisely\nat the bifurcation points, while the bi-partite entanglement changes slope at\nthese points. We have also investigated the connection between entanglement and\nthe fixed points on the branch of the bifurcation diagram between the two first\nbifurcation points and we found that the entanglement measures take their\nextreme values precisely on these points. We conjecture that our results on\nthis behaviour of entanglement is generic for many quantum systems with a\nnon-linear classical analogue.",
"arxiv_id": "quant-ph/0702172",
"authors": [
"George Stamatiou",
"Demetris P. K. Ghikas"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.physleta.2007.04.003",
"title": "Quantum Entanglement dependence on bifurcations and scars in non autonomous systems. The case of Quantum Kicked Top",
"url": "https://arxiv.org/abs/quant-ph/0702172"
},
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