发表机构
LMIB(Beihang University), Ministry of Education, School of Mathematical Sciences, Beihang University（北京航空航天大学数学科学学院，教育部拉格朗日计算几何与应用重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过图论方法研究不可扩展正交矩阵，系统构造了多量子比特不可扩展乘积基，并确定了所有维度下的完整规模谱。
AI 中文摘要
多量子比特不可扩展乘积基（UPB）的构造一直是一个长期存在的问题。我们通过研究其不可扩展正交矩阵（UOM）并采用图论方法，给出了多量子比特UPB的系统构造。小规模UOM的行分解产生了主要区间。完成图解决了其余较小的UPB规模，除了一个由良好的列结构获得的规模。其他UPB规模的不存在性则通过纤维和行对的计数得出。计算机仅用于少数有限的UOM检查，其精确测试在证书附录中说明。这些论证确定了每个维度中完整的多量子比特UPB规模谱。
英文摘要
The construction of multiqubit unextendible product bases (UPBs) has been a long-standing problem. We give a systematic construction of multiqubit UPBs by studying their unextendible orthogonal matrices (UOMs) with graph-theoretic methods. Row decompositions of small UOMs produce the main intervals. Com- pletion graphs settle the remaining small UPB sizes, except for one size obtained from a good column structure. Nonexistence of the other UPB sizes follows from counts of fibres and row pairs. The computer is used only for a few finite UOM checks, whose exact tests are stated in the certificate appendix. These arguments determine the complete multiqubit UPB size spectrum in every dimension.
