Multipartite-to-bipartite entanglement transformations and polynomial identity testing

Multipartite-to-bipartite entanglement transformations and polynomial identity testing. Chitambar, E., Duan, R., & Shi, Y. Physical Review A - Atomic, Molecular, and Optical Physics, 2010.
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We consider the problem of deciding if some multiparty entangled pure state can be converted, with a nonzero success probability, into a given bipartite pure state shared between two specified parties through local quantum operations and classical communication. We show that this question is equivalent to the well-known computational problem of deciding if a multivariate polynomial is identically zero. Efficient randomized algorithms developed to study the latter can thus be applied to our question. As a result, a given transformation is possible if and only if it is generically attainable by a simple randomized protocol. © 2010 The American Physical Society.

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 title = {Multipartite-to-bipartite entanglement transformations and polynomial identity testing},
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 year = {2010},
 volume = {81},
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 abstract = {We consider the problem of deciding if some multiparty entangled pure state can be converted, with a nonzero success probability, into a given bipartite pure state shared between two specified parties through local quantum operations and classical communication. We show that this question is equivalent to the well-known computational problem of deciding if a multivariate polynomial is identically zero. Efficient randomized algorithms developed to study the latter can thus be applied to our question. As a result, a given transformation is possible if and only if it is generically attainable by a simple randomized protocol. © 2010 The American Physical Society.},
 bibtype = {article},
 author = {Chitambar, E. and Duan, R. and Shi, Y.},
 doi = {10.1103/PhysRevA.81.052310},
 journal = {Physical Review A - Atomic, Molecular, and Optical Physics},
 number = {5}
}

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