Nonexistence of n-qubit unextendible product bases of size \(2^n-5\)

  • Lin Chen
  • Dragomir Ž. Đoković


It is known that the n-qubit system has no unextendible product bases (UPBs) of cardinality \(2^n-1\), \(2^n-2\) and \(2^n-3\). On the other hand, the n-qubit UPBs of cardinality \(2^n-4\) exist for all \(n\ge 3\). We prove that they do not exist for cardinality \(2^n-5\).


Unextendible product basis (UPB) Multiqubit Positive partial transpose (PPT) 



LC was supported by Beijing Natural Science Foundation (4173076), the NNSF of China (Grant No. 11501024), and the Fundamental Research Funds for the Central Universities (Grant Nos. KG12001101, ZG216S1760 and ZG226S17J6). The second author was supported in part by the National Sciences and Engineering Research Council (NSERC) of Canada Discovery Grant 5285.


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Authors and Affiliations

  1. 1.School of Mathematics and Systems ScienceBeihang UniversityBeijingChina
  2. 2.International Research Institute for Multidisciplinary ScienceBeihang UniversityBeijingChina
  3. 3.Department of Pure Mathematics and Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada

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