dorsal/arxiv
View SchemaConnections and Metrics Respecting Standard Purification
| Authors | J. Dittmann, A. Uhlmann |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9806028 |
| URL | https://arxiv.org/abs/quant-ph/9806028 |
| DOI | 10.1063/1.532884 |
| Journal | J.Math.Phys. 40 (1999) 3246-3267 |
Abstract
Standard purification interlaces Hermitian and Riemannian metrics on the space of density operators with metrics and connections on the purifying Hilbert-Schmidt space. We discuss connections and metrics which are well adopted to purification, and present a selected set of relations between them. A connection, as well as a metric on state space, can be obtained from a metric on the purification space. We include a condition, with which this correspondence becomes one-to-one. Our methods are borrowed from elementary *-representation and fibre space theory. We lift, as an example, solutions of a von Neumann equation, write down holonomy invariants for cyclic ones, and ``add noise'' to a curve of pure states.
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"abstract": "Standard purification interlaces Hermitian and Riemannian metrics on the\nspace of density operators with metrics and connections on the purifying\nHilbert-Schmidt space. We discuss connections and metrics which are well\nadopted to purification, and present a selected set of relations between them.\nA connection, as well as a metric on state space, can be obtained from a metric\non the purification space. We include a condition, with which this\ncorrespondence becomes one-to-one. Our methods are borrowed from elementary\n*-representation and fibre space theory. We lift, as an example, solutions of a\nvon Neumann equation, write down holonomy invariants for cyclic ones, and ``add\nnoise\u0027\u0027 to a curve of pure states.",
"arxiv_id": "quant-ph/9806028",
"authors": [
"J. Dittmann",
"A. Uhlmann"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.532884",
"journal_ref": "J.Math.Phys. 40 (1999) 3246-3267",
"title": "Connections and Metrics Respecting Standard Purification",
"url": "https://arxiv.org/abs/quant-ph/9806028"
},
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