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Conditions for a class of entanglement transformations

M. A. Nielsen
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Abstract

Suppose Alice and Bob jointly possess a pure state, $|ψ\ra$. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform $|ψ\ra$ into another joint state $|ϕ\ra$. This Letter gives necessary and sufficient conditions for this process of entanglement transformation to be possible. These conditions reveal a partial ordering on the entangled states, and connect quantum entanglement to the algebraic theory of majorization. As a consequence, we find that there exist essentially different types of entanglement for bipartite quantum systems.

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M. A. Nielsen. 1999-08-17. Conditions for a class of entanglement transformations. https://doi.org/10.1103/physrevlett.83.436

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