Communications in Mathematical Physics

, Volume 333, Issue 1, pp 351–365

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


DOI: 10.1007/s00220-014-2186-7

Cite this article as:
Chen, J. & Johnston, N. Commun. Math. Phys. (2015) 333: 351. doi:10.1007/s00220-014-2186-7


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.

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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