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Published April 2008 | Published
Journal Article Open

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

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.

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.

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