Relation Between Catalyst-assisted Entanglement Transformation and Multiple-copy Transformation

Abstract

We show that in some cases, catalyst-assisted entanglement transformation cannot be implemented by multiple-copy transformation for pure states. This fact, together with the result we obtained in [R. Y. Duan, Y. Feng, X. Li, and M. S. Ying, Phys. Rev. A 71, 042319 (2005)] that the latter can be completely implemented by the former, indicates that catalyst-assisted transformation is strictly more powerful than multiple-copy transformation. For purely probabilistic setting we find, however, these two kinds of transformations are geometrically equivalent in the sense that the sets of pure states which can be converted into a given pure state with maximal probabilities not less than a given value have the same closure, no matter catalyst-assisted transformation or multiple-copy transformation is used.

7 pages, journal version

References in corpus (6)

• The trumping relation and the structure of the bipartite entangled states
• Multiple-copy entanglement transformation and entanglement catalysis
• A classification of incomparable states
• Catalyst-assisted Probabilistic Entanglement Transformation
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• Stochastic domination for iterated convolutions and catalytic majorization
• Matrix Majorization in Large Samples with Varying Support Restrictions
• Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of $\alpha$-z Relative Entropies