Communications in Mathematical Physics

, Volume 333, Issue 1, pp 351–365 | Cite as

The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases)

Article

Abstract

A long-standing open question asks for the minimum number of vectors needed to form an unextendible product basis in a given bipartite or multipartite Hilbert space. A partial solution was found by Alon and Lovász (J. Comb. Theory Ser. A, 95:169–179, 2001), but since then only a few other cases have been solved. We solve all remaining bipartite cases, as well as a large family of multipartite cases.

Keywords

Minimum Size Orthogonality Condition Permutation Matrix Positive Partial Transpose Nonzero Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of GuelphGuelphCanada
  2. 2.Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  3. 3.UTS-AMSS Joint Research Laboratory for Quantum Computation and Quantum Information ProcessingAcademy of Mathematics and Systems Science, Chinese Academy of SciencesBeijingChina

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