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Correlated entanglement distillation and the structure of the set of undistillable states

Brandão, F. G. S. L. and Eisert, J. (2008) Correlated entanglement distillation and the structure of the set of undistillable states. Journal of Mathematical Physics, 49 (4). Art. No. 042102. ISSN 0022-2488. doi:10.1063/1.2888925. https://resolver.caltech.edu/CaltechAUTHORS:20160524-091208947

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Abstract

We consider entanglement distillation under the assumption that the input states are allowed to be correlated among each other. We hence replace the usually considered independent and identically distributed hypothesis by the weaker assumption of merely having identical reductions. We find that whether a state is then distillable or not is only a property of these reductions, and not of the correlations that are present in the input state. This is shown by establishing an appealing relation between the set of copy-correlated undistillable states and the standard set of undistillable states: The former turns out to be the convex hull of the latter. As an example of the usefulness of our approach to the study of entanglement distillation, we prove a new activation result, which generalizes earlier findings: It is shown that for every entangled state σ and every k, there exists a copy-correlated k-undistillable state ρ such that σ⊗ρ is single-copy distillable. Finally, the relation of our results to the conjecture about the existence of bound entangled states with a nonpositive partial transpose is discussed.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.2888925DOIArticle
http://scitation.aip.org/content/aip/journal/jmp/49/4/10.1063/1.2888925PublisherArticle
ORCID:
AuthorORCID
Brandão, F. G. S. L.0000-0003-3866-9378
Additional Information:© 2008 American Institute of Physics. Received 7 October 2007; accepted 24 January 2008; published online 9 April 2008. We acknowledge fruitful and interesting conversations with a number of people on these and very closely related topics, among them D. Gottesman, D. Gross, M. Horodecki, Ll. Masanes, B. Terhal, J. Oppenheim, M. Piani, M.B. Plenio, S. Virmani, K. G. H. Vollbrecht, and R. F. Werner. This work has been supported by the EU (QAP), the Royal Society, the QIP-IRC, Microsoft Research, the Brazilian agency CNPq, and the EURYI Award Scheme.
Funders:
Funding AgencyGrant Number
European UnionUNSPECIFIED
Royal SocietyUNSPECIFIED
QIP-IRCUNSPECIFIED
Microsoft ResearchUNSPECIFIED
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)UNSPECIFIED
EURYI Award SchemeUNSPECIFIED
Issue or Number:4
DOI:10.1063/1.2888925
Record Number:CaltechAUTHORS:20160524-091208947
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160524-091208947
Official Citation:Correlated entanglement distillation and the structure of the set of undistillable states Brandão, F. G. S. L. and Eisert, J., Journal of Mathematical Physics, 49, 042102 (2008), DOI:http://dx.doi.org/10.1063/1.2888925
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67293
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 May 2016 16:38
Last Modified:11 Nov 2021 00:30

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