2004/04/07 by Runyao Duan, Yuan Feng, Duan, Runyao +3
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0404046
Now 19 pages. Need IEEEtran.cls. Results in the case of probabilistic transformations added. Presentation part improved
openalex publication_date 2004/04/07 · arxiv created 2005/01/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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× 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× 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.