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arXiv:1711.11056 · Physical Review X

Transformations among Pure Multipartite Entangled States via Local Operations are Almost Never Possible

David Sauerwein, Nolan R. Wallach, Gilad Gour, Barbara Kraus

Published Jul 23, 2018• 76 citations
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Abstract

A comprehensive characterization of ``local operations assisted by classical communication'' shows that pure multipartite entangled states cannot be transformed into other similar states, an important insight in entanglement theory.
DOI
10.1103/physrevx.8.031020

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Transformations involving only local operations assisted with classical communication are investigated for multipartite entangled pure states having tensor rank 2. All necessary and sufficient conditions for the possibility of deterministically converting truly multipartite, rank-2 states into each other are given. Furthermore, a chain of local operations that successfully achieves the transformation has been identified for all allowed transformations. The identified chains have two nice features: (1) each party needs to carry out at most one local operation and (2) all of these local operations are also deterministic transformations by themselves. Finally, it is found that there are disjoint classes of states, all of which can be identified by a single real parameter, which remain invariant under deterministic transformations.