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One-Shot Rates for Entanglement Manipulation Under Non-entangling Maps

Brandão, Fernando G. S. L. and Datta, Nilanjana (2011) One-Shot Rates for Entanglement Manipulation Under Non-entangling Maps. IEEE Transactions on Information Theory, 57 (3). pp. 1754-1760. ISSN 0018-9448. doi:10.1109/TIT.2011.2104531.

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We obtain expressions for the optimal rates of one-shot entanglement manipulation under operations which generate a negligible amount of entanglement. As the optimal rates for entanglement distillation and dilution in this paradigm, we obtain the max- and min-relative entropies of entanglement, the two logarithmic robustnesses of entanglement, and smoothed versions thereof. This gives a new operational meaning to these entanglement measures. Moreover, by considering the limit of many identical copies of the shared entangled state, we partially recover the recently found reversibility of entanglement manipulation under the class of operations which asymptotically do not generate entanglement.

Item Type:Article
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URLURL TypeDescription Paper
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2011 IEEE. Manuscript received May 18, 2009; revised October 22, 2010; accepted October 30, 2010. Date of current version February 18, 2011. This work is part of the QIP-IRC supported by the European Community’s Seventh Framework Programme (FP7/2007-2013) under Grant Agreement Number 213681, EPSRC (GR/S82176/0) as well as the Integrated Project Qubit Applications (QAP) supported by the IST directorate as Contract Number 015848. The work of F. G. S. L. Brandão was supported by a Conhecimento Novo fellowship from Fundação de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG). The authors would like to thank Martin Plenio for many interesting discussions on the theme of this paper.
Funding AgencyGrant Number
European Commission213681
Engineering and Physical Sciences Research Council (EPSRC)GR/S82176/0
IST directorate015848
Fundação de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG)UNSPECIFIED
Subject Keywords:Entanglement manipulation, non-entangling maps, logarithmic robustness, min- and max-relative entropies of entanglement
Issue or Number:3
Record Number:CaltechAUTHORS:20160525-155015519
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Official Citation:F. G. S. L. Brandao and N. Datta, "One-Shot Rates for Entanglement Manipulation Under Non-entangling Maps," in IEEE Transactions on Information Theory, vol. 57, no. 3, pp. 1754-1760, March 2011. doi: 10.1109/TIT.2011.2104531
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67369
Deposited By: Tony Diaz
Deposited On:26 May 2016 19:35
Last Modified:11 Nov 2021 00:31

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