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

被引：54
作者：
Chen, Jianxin [1 ,2 ,3 ]
Johnston, Nathaniel [2 ]
机构：
[1] Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada
[2] Univ Waterloo, Inst Quantum Comp, Waterloo, ON N2L 3G1, Canada
[3] Chinese Acad Sci, Acad Math & Syst Sci, UTS AMSS Joint Res Lab Quantum Computat & Quantum, Beijing, Peoples R China
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2015年 / 333卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Minimum Size; Orthogonality Condition; Permutation Matrix; Positive Partial Transpose; Nonzero Product;
D O I：
10.1007/s00220-014-2186-7
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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 (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.
引用
收藏
页码：351 / 365
页数：15
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