When is there a multipartite maximum entangled state?

  • Authors:

  • Runyao Duan;Yaoyun Shi

  • Affiliations:

  • Centre for Quantum Computation and Int. Systems, Faculty of Eng. and Information Techn., Univ. of Techn., Sydney, NSW, Australia and Dept. of Computer Science and Techn., Tsinghua National Lab. fo ...;Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2010

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Abstract

For a multipartite quantum system of the dimension d1 ⊗ d2 ⊗ ... ⊗ dn, where d1 ≥d2 ≥ ... ≥ dn ≥ 2, is there an entangled state maximum in the sense that all otherstates in the system can be obtained from the state through local quantum operationsand classical communications (LOCC)? When d1 ≥ πi=2ndi such state exists. We showthat this condition is also necessary. Our proof, somewhat surprisingly, uses results fromalgebraic complexity theory.