Unextendible maximally entangled bases in \({\mathbb {C}}^{pd}\otimes {\mathbb {C}}^{qd}\)

  • Gui-Jun Zhang
  • Yuan-Hong TaoEmail author
  • Yi-Fan Han
  • Xin-Lei Yong
  • Shao-Ming Fei


The construction of unextendible maximally entangled bases is tightly related to quantum information processing like local state discrimination. We put forward two constructions of UMEBs in \({\mathbb {C}}^{pd}\otimes {\mathbb {C}}^{qd}\)(\(p\le q\)) based on the constructions of UMEBs in \({\mathbb {C}}^{d}\otimes {\mathbb {C}}^{d}\) and in \({\mathbb {C}}^{p}\otimes {\mathbb {C}}^{q}\), which generalizes the results in Guo (Phys Rev A 94:052302, 2016) by two approaches. Two different 48-member UMEBs in \({\mathbb {C}}^{6}\otimes {\mathbb {C}}^{9}\) have been constructed in detail.


Unextendible maximally entangled bases Bipartite system Quantum entanglement Schmidt number 



The work is supported by the NSFC under Nos. 11675113, 11761073 and NSF of Beijing under No. KZ201810028042.

Author Contributions

G.-J.Z and Y.-H.T. wrote the main manuscript text. All of the authors reviewed the manuscript.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Gui-Jun Zhang
    • 1
  • Yuan-Hong Tao
    • 1
    Email author
  • Yi-Fan Han
    • 1
  • Xin-Lei Yong
    • 1
  • Shao-Ming Fei
    • 2
    • 3
  1. 1.Department of Mathematics, College of SciencesYanbian UniversityYanjiChina
  2. 2.School of Mathematics SciencesCapital Normal UniversityBeijingChina
  3. 3.Max-Planck-Institute for Mathematics in the ScienceLeipzigGermany

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