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New constructions of unextendible entangled bases with fixed Schmidt number

  • Xinlei Yong
  • Yiyang Song
  • Yuanhong TaoEmail author
Article
  • 27 Downloads

Abstract

We study the unextendible entangled bases with fixed Schmidt number (UEBk) in \(\mathbb {C}^d\otimes \mathbb {C}^{d'}\) which play a significant role in quantum information processing. We first give the construction of the UEBk when \(d'\) is not the multiple of k and illustrate two different UEBks in \(\mathbb {C}^3\otimes \mathbb {C}^7\) and \(\mathbb {C}^4\otimes \mathbb {C}^{10}\). Then, we present the construction of the UEBk when \(d'\) is the multiple of k and illustrate them in \(\mathbb {C}^7\otimes \mathbb {C}^8\), \(\mathbb {C}^4\otimes \mathbb {C}^9\), \(\mathbb {C}^8\otimes \mathbb {C}^8\) and \(\mathbb {C}^4\otimes \mathbb {C}^8\). Our constructions of UEBk generalize the results in Guo [Phys Rev A 90 : 054303, 2014].

Keywords

Unextendible entangled bases with fixed Schmidt number (UEBk) Quantum entanglement Schmidt number 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesYanbian UniversityYanjiChina

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