An Equivalence of Entanglement-Assisted Transformation and Multiple-Copy Entanglement Transformation

Abstract

We examine the powers of entanglement-assisted transformation and multiple-copy entanglement transformation. First, we find a sufficient condition of when a given catalyst is useful in producing another specific target state. As an application of this condition, for any non-maximally entangled bipartite pure state and any integer $n$ not less than 4, we are able to explicitly construct a set of $n\times n$ quantum states which can be produced by using the given state as a catalyst. Second, we prove that for any positive integer $k$, entanglement-assisted transformation with $k\times k$-dimensional catalysts is useful in producing a target state if and only if multiple-copy entanglement transformation with $k$ copies of state is useful in producing the same target. Moreover, a necessary and sufficient condition for both of them is obtained in terms of the Schmidt coefficients of the target. This equivalence of entanglement-assisted transformation and multiple-copy entanglement transformation implies many interesting properties of entanglement transformation. Furthermore, these results are generalized to the case of probabilistic entanglement transformations.

Now 19 pages. Need IEEEtran.cls. Results in the case of probabilistic transformations added. Presentation part improved

References in corpus (7)

• Concentrating Partial Entanglement by Local Operations
• Conditions for a class of entanglement transformations
• Entanglement of pure states for a single copy
• Entanglement-assisted local manipulation of pure quantum states
• The trumping relation and the structure of the bipartite entangled states
• Multiple-copy entanglement transformation and entanglement catalysis
• More Is Not Necessarily Easier

Cited by in corpus (1)

• Catalysis of entanglement and other quantum resources