dorsal/arxiv
View SchemaA dual de Finetti theorem
| Authors | Graeme Mitchison |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701064 |
| URL | https://arxiv.org/abs/quant-ph/0701064 |
Abstract
The quantum de Finetti theorem says that, given a symmetric state, the state obtained by tracing out some of its subsystems approximates a convex sum of power states. The more subsystems are traced out, the better this approximation becomes. Schur-Weyl duality suggests that there ought to be a dual result that applies to a unitarily invariant state rather than a symmetric state. Instead of tracing out a number of subsystems, one traces out part of every subsystem. The theorem then asserts that the resulting state approximates the fully mixed state, and the larger the dimension of the traced-out part of each subsystem, the better this approximation becomes. This paper gives a number of propositions together with their dual versions, to show how far the duality holds.
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"abstract": "The quantum de Finetti theorem says that, given a symmetric state, the state\nobtained by tracing out some of its subsystems approximates a convex sum of\npower states. The more subsystems are traced out, the better this approximation\nbecomes. Schur-Weyl duality suggests that there ought to be a dual result that\napplies to a unitarily invariant state rather than a symmetric state. Instead\nof tracing out a number of subsystems, one traces out part of every subsystem.\nThe theorem then asserts that the resulting state approximates the fully mixed\nstate, and the larger the dimension of the traced-out part of each subsystem,\nthe better this approximation becomes. This paper gives a number of\npropositions together with their dual versions, to show how far the duality\nholds.",
"arxiv_id": "quant-ph/0701064",
"authors": [
"Graeme Mitchison"
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"title": "A dual de Finetti theorem",
"url": "https://arxiv.org/abs/quant-ph/0701064"
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