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Mathematical structure of entanglement catalysis

Daftaur, Sumit and Klimesh, Matthew (2001) Mathematical structure of entanglement catalysis. Physical Review A, 64 (4). Art. No. 042314. ISSN 1050-2947. doi:10.1103/PhysRevA.64.042314.

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The majorization relation has been shown to be useful in classifying which transformations of jointly held quantum states are possible using local operations and classical communication. In some cases, a direct transformation between two states is not possible, but it becomes possible in the presence of another state (known as a catalyst); this situation is described mathematically by the trumping relation, an extension of majorization. The structure of the trumping relation is not nearly as well understood as that of majorization. We give an introduction to this subject and derive some results. Most notably, we show that the dimension of the required catalyst is, in general, unbounded; there is no integer k such that it suffices to consider catalysts of dimension k or less in determining which states can be catalyzed into a given state. We also show that almost all bipartite entangled states are potentially useful as catalysts.

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Additional Information:©2001 The American Physical Society Received 24 April 2001; published 18 September 2001 The authors thank Michael Nielsen for introducing us to this subject, providing encouragement and feedback on our results, and generously commenting on the manuscript. We also thank David Beckman for helpful discussions.
Issue or Number:4
Record Number:CaltechAUTHORS:DAFpra01
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2801
Deposited By: Archive Administrator
Deposited On:27 Apr 2006
Last Modified:08 Nov 2021 19:51

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