Multipartite-to-bipartite entanglement transformations and polynomial identity testing

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Journal Article
Physical Review A - Atomic, Molecular, and Optical Physics, 2010, 81 (5)
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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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