dorsal/arxiv
View SchemaA most compendious and facile quantum de Finetti theorem
| Authors | Robert Koenig, Graeme Mitchison |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0703210 |
| URL | https://arxiv.org/abs/quant-ph/0703210 |
| Journal | J. Math. Phys. 50, 012105 (2009) |
Abstract
In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's "exponential" approximation by "almost-product" states, a theorem which deals with certain triples of representations of the unitary group, and D'Cruz et al.'s result for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choice of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states, and leads to some new results, including an exponential theorem for infinite-dimensional systems.
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"abstract": "In its most basic form, the finite quantum de Finetti theorem states that the\nreduced k-partite density operator of an n-partite symmetric state can be\napproximated by a convex combination of k-fold product states. Variations of\nthis result include Renner\u0027s \"exponential\" approximation by \"almost-product\"\nstates, a theorem which deals with certain triples of representations of the\nunitary group, and D\u0027Cruz et al.\u0027s result for infinite-dimensional systems. We\nshow how these theorems follow from a single, general de Finetti theorem for\nrepresentations of symmetry groups, each instance corresponding to a particular\nchoice of symmetry group and representation of that group. This gives some\ninsight into the nature of the set of approximating states, and leads to some\nnew results, including an exponential theorem for infinite-dimensional systems.",
"arxiv_id": "quant-ph/0703210",
"authors": [
"Robert Koenig",
"Graeme Mitchison"
],
"categories": [
"quant-ph"
],
"journal_ref": "J. Math. Phys. 50, 012105 (2009)",
"title": "A most compendious and facile quantum de Finetti theorem",
"url": "https://arxiv.org/abs/quant-ph/0703210"
},
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