Multipartite-to-bipartite entanglement transformations and polynomial identity testing. Chitambar, E., Duan, R., & Shi, Y. Physical Review A - Atomic, Molecular, and Optical Physics, 81(5):1-4, 2010.
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We consider the problem of deciding if a given three-party entangled pure state can be converted, with a non-zero success probability, into a given two-party pure state 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 the question of tripartite to bipartite entanglement transformations.
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 title = {Multipartite-to-bipartite entanglement transformations and polynomial identity testing},
 type = {article},
 year = {2010},
 pages = {1-4},
 volume = {81},
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 abstract = {We consider the problem of deciding if a given three-party entangled pure state can be converted, with a non-zero success probability, into a given two-party pure state 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 the question of tripartite to bipartite entanglement transformations.},
 bibtype = {article},
 author = {Chitambar, Eric and Duan, Runyao and Shi, Yaoyun},
 doi = {10.1103/PhysRevA.81.052310},
 journal = {Physical Review A - Atomic, Molecular, and Optical Physics},
 number = {5}
}

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