Physics – Quantum Physics
Scientific paper
2007-09-24
J. Math. Phys. 49, 042102 (2008)
Physics
Quantum Physics
10 pages, 3 figures, replaced with published version
Scientific paper
10.1063/1.2888925
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 and every positive integer k, there exists a copy-correlated k-undistillable state such that their tensor product is single-copy distillable. Finally, the relation of our results to the conjecture about the existence of bound entangled states with a non-positive partial transpose is discussed.
Brandao Fernando G. S. L.
Eisert Jens
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