dorsal/arxiv
View SchemaAn Equivalence of Entanglement-Assisted Transformation and Multiple-Copy Entanglement Transformation
| Authors | Runyao Duan, Yuan Feng, Mingsheng Ying |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0404046 |
| URL | https://arxiv.org/abs/quant-ph/0404046 |
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.
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"abstract": "We examine the powers of entanglement-assisted transformation and\nmultiple-copy entanglement transformation. First, we find a sufficient\ncondition of when a given catalyst is useful in producing another specific\ntarget state. As an application of this condition, for any non-maximally\nentangled bipartite pure state and any integer $n$ not less than 4, we are able\nto explicitly construct a set of $n\\times n$ quantum states which can be\nproduced by using the given state as a catalyst. Second, we prove that for any\npositive integer $k$, entanglement-assisted transformation with $k\\times\nk$-dimensional catalysts is useful in producing a target state if and only if\nmultiple-copy entanglement transformation with $k$ copies of state is useful in\nproducing the same target. Moreover, a necessary and sufficient condition for\nboth of them is obtained in terms of the Schmidt coefficients of the target.\nThis equivalence of entanglement-assisted transformation and multiple-copy\nentanglement transformation implies many interesting properties of entanglement\ntransformation. Furthermore, these results are generalized to the case of\nprobabilistic entanglement transformations.",
"arxiv_id": "quant-ph/0404046",
"authors": [
"Runyao Duan",
"Yuan Feng",
"Mingsheng Ying"
],
"categories": [
"quant-ph"
],
"title": "An Equivalence of Entanglement-Assisted Transformation and Multiple-Copy Entanglement Transformation",
"url": "https://arxiv.org/abs/quant-ph/0404046"
},
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