@article {1440, title = {The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases) }, journal = {Communications in Mathematical Physics}, volume = {333}, year = {2015}, month = {2014/10/10}, pages = {351 - 365}, 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 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. }, doi = {10.1007/s00220-014-2186-7}, url = {http://arxiv.org/abs/1301.1406v1}, author = {Jianxin Chen and Nathaniel Johnston} }