dorsal/arxiv
View SchemaA General Setting for Geometric Phase of Mixed States Under an Arbitrary Nonunitary Evolution
| Authors | A. T. Rezakhani, P. Zanardi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507280 |
| URL | https://arxiv.org/abs/quant-ph/0507280 |
| DOI | 10.1103/PhysRevA.73.012107 |
| Journal | Phys. Rev. A 73, 012107 (2006) |
Abstract
The problem of geometric phase for an open quantum system is reinvestigated in a unifying approach. Two of existing methods to define geometric phase, one by Uhlmann's approach and the other by kinematic approach, which have been considered to be distinct, are shown to be related in this framework. The method is based upon purification of a density matrix by its uniform decomposition and a generalization of the parallel transport condition obtained from this decomposition. It is shown that the generalized parallel transport condition can be satisfied when Uhlmann's condition holds. However, it does not mean that all solutions of the generalized parallel transport condition are compatible with those of Uhlmann's one. It is also shown how to recover the earlier known definitions of geometric phase as well as how to generalize them when degeneracy exists and varies in time.
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"abstract": "The problem of geometric phase for an open quantum system is reinvestigated\nin a unifying approach. Two of existing methods to define geometric phase, one\nby Uhlmann\u0027s approach and the other by kinematic approach, which have been\nconsidered to be distinct, are shown to be related in this framework. The\nmethod is based upon purification of a density matrix by its uniform\ndecomposition and a generalization of the parallel transport condition obtained\nfrom this decomposition. It is shown that the generalized parallel transport\ncondition can be satisfied when Uhlmann\u0027s condition holds. However, it does not\nmean that all solutions of the generalized parallel transport condition are\ncompatible with those of Uhlmann\u0027s one. It is also shown how to recover the\nearlier known definitions of geometric phase as well as how to generalize them\nwhen degeneracy exists and varies in time.",
"arxiv_id": "quant-ph/0507280",
"authors": [
"A. T. Rezakhani",
"P. Zanardi"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.012107",
"journal_ref": "Phys. Rev. A 73, 012107 (2006)",
"title": "A General Setting for Geometric Phase of Mixed States Under an Arbitrary Nonunitary Evolution",
"url": "https://arxiv.org/abs/quant-ph/0507280"
},
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