Multipartite-to-bipartite entanglement transformations and polynomial identity testing

Eric Chitambar, Runyao Duan, and Yaoyun Shi
Phys. Rev. A 81, 052310 – Published 10 May 2010

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.

  • Received 4 August 2009

DOI:https://doi.org/10.1103/PhysRevA.81.052310

©2010 American Physical Society

Authors & Affiliations

Eric Chitambar1,*, Runyao Duan2,†, and Yaoyun Shi3,‡

  • 1Physics Department, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040, USA
  • 2Centre for Quantum Computation and Intelligent Systems (QCIS), Faculty of Engineering and Information Technology, University of Technology, Sydney, New South Wales 2007, Australia, and State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, People’s Republic of China
  • 3Department of Electrical Engineering and Computer Science, University of Michigan, 2260 Hayward Street, Ann Arbor, Michigan 48109-2121, USA

  • *echitamb@umich.edu
  • Runyao.Duan@uts.edu.au
  • shiyy@eecs.umich.edu

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Vol. 81, Iss. 5 — May 2010

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