A Proof for the Existence of Nonsquare Unextendible Maximally Entangled Bases

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Abstract

The nonsquare unextendible maximally entangled basis (nUMEB) is a set of orthonormal maximally entangled states in \(C^{d}\otimes C^{d^{\prime }}~(d^{\prime }> d)\) which have no additional maximally entangled vectors orthogonal to all of them. We study nUMEBs in arbitrary bipartite spaces and present a constructive proof of the existence of nUMEBs in \(C^{d}\otimes C^{d^{\prime }}~(d^{\prime }\geq 2d)\). Furthermore, a bound condition for the existence of nUMEBs for \(C^{d}\otimes C^{d^{\prime }}~(d^{\prime }\geq 2d)\) is obtained.

Keywords

Unextendible maximally entangled basis Orthonormal maximally entangled states Maximally entangled vector 

Notes

Acknowledgements

This work is supported by the Natural Science Foundation of China (Grant No. 61771294) and Shandong Provincial Natural Science Foundation, China (Grant No. ZR2015FQ006).

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

Authors and Affiliations

  1. 1.College of Mathematic and Information ScienceShandong Technology and Business UniversityYantaiChina

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