%0 Journal Article %J Communications in Mathematical Physics %D 2015 %T The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases) %A Jianxin Chen %A Nathaniel Johnston %X 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 Lovasz in 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. %B Communications in Mathematical Physics %V 333 %P 351 - 365 %8 2014/10/10 %G eng %U http://arxiv.org/abs/1301.1406v1 %N 1 %! Commun. Math. Phys. %R 10.1007/s00220-014-2186-7