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A most compendious and facile quantum de Finetti theorem

König, Robert and Mitchison, Graeme (2009) A most compendious and facile quantum de Finetti theorem. Journal of Mathematical Physics, 50 (1). 012105. ISSN 0022-2488. doi:10.1063/1.3049751.

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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 the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] 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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Additional Information:© 2009 American Institute of Physics. Received 24 March 2008; accepted 24 November 2008; published 12 January 2009. We thank Matthias Christandl, Ignacio Cirac, Tobias Osborne, and Renato Renner for helpful discussions. We also thank the reviewers for their comments. This work was supported by the EU project RESQ (Grant No. IST-2001-37559) and the European Commission through the FP6-FET Integrated Project SCALA, Grant No. CT-015714. R.K. acknowledges support from NSF Grant No. PHY-0456720 and PHY-0803371. G.M. acknowledges support from the project PROSECCO (Grant No. IST-2001-39227) of the IST-FET programme of the EC.
Funding AgencyGrant Number
European Union (EU)IST-2001-37559
European CommissionCT-015714
European Commission (EC)IST-2001-39227
Subject Keywords:quantum theory
Issue or Number:1
Record Number:CaltechAUTHORS:20090420-153602741
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14034
Deposited By: Tony Diaz
Deposited On:21 Apr 2009 16:28
Last Modified:08 Nov 2021 22:42

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