Pawel Horodecki, Marcin L. Nowakowski
Published 2005-03-07, updated 2007-02-27Version 2
Basing on states and channels isomorphism we point out that semidefinite programming can be used as a quick test for nonzero one-way quantum channel capacity. This can be achieved by search of symmetric extensions of states isomorphic to a given quantum channel. With this method we provide examples of quantum channels that can lead to high entanglement transmission but still have zero one-way capacity, in particular, regions of symmetric extendibility for isotropic states in arbitrary dimensions are presented. Further we derive {\it a new entanglement parameter} based on (normalised) relative entropy distance to the set of states that have symmetric extensions and show explicitly the symmetric extension of isotropic states being the nearest to singlets in the set of symmetrically extendible states. The suitable regularisation of the parameter provides a new upper bound on one-way distillable entanglement.
Comments: 6 pages, no figures, RevTeX4. Signifficantly corrected version. Claim on continuity of channel capacities removed due to flaw in the corresponding proof. Changes and corrections performed in the part proposing a new upper bound on one-way distillable etanglement which happens to be not one-way entanglement monotone
Journal: J. Phys. A: Math. Theor. 42 (2009) 135306
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