dorsal/arxiv
View SchemaMixed state geometric phases, entangled systems, and local unitary transformations
| Authors | Marie Ericsson, Arun K. Pati, Erik Sjöqvist, Johan Brännlund, Daniel. K. L. Oi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0206063 |
| URL | https://arxiv.org/abs/quant-ph/0206063 |
| DOI | 10.1103/PhysRevLett.91.090405 |
| Journal | Phys. Rev. Lett. 91, 090405 (2003) |
Abstract
The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution not only depends on the geometry of the path of the system alone but also on a constrained bi-local unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires uni-local transformations and is therefore essentially a property of the system alone.
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"abstract": "The geometric phase for a pure quantal state undergoing an arbitrary\nevolution is a ``memory\u0027\u0027 of the geometry of the path in the projective Hilbert\nspace of the system. We find that Uhlmann\u0027s geometric phase for a mixed quantal\nstate undergoing unitary evolution not only depends on the geometry of the path\nof the system alone but also on a constrained bi-local unitary evolution of the\npurified entangled state. We analyze this in general, illustrate it for the\nqubit case, and propose an experiment to test this effect. We also show that\nthe mixed state geometric phase proposed recently in the context of\ninterferometry requires uni-local transformations and is therefore essentially\na property of the system alone.",
"arxiv_id": "quant-ph/0206063",
"authors": [
"Marie Ericsson",
"Arun K. Pati",
"Erik Sj\u00f6qvist",
"Johan Br\u00e4nnlund",
"Daniel. K. L. Oi"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevLett.91.090405",
"journal_ref": "Phys. Rev. Lett. 91, 090405 (2003)",
"title": "Mixed state geometric phases, entangled systems, and local unitary transformations",
"url": "https://arxiv.org/abs/quant-ph/0206063"
},
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