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New constructions of unextendible entangled bases with fixed Schmidt number

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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].

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Yanbian University, Yanji, 133002, China

    Xinlei Yong, Yiyang Song & Yuanhong Tao

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  1. Xinlei Yong
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  2. Yiyang Song
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Correspondence to Yuanhong Tao.

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This work is supported by Natural Science Foundation of China under Number 11761073.

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Yong, X., Song, Y. & Tao, Y. New constructions of unextendible entangled bases with fixed Schmidt number. Quantum Inf Process 18, 337 (2019). https://doi.org/10.1007/s11128-019-2451-y

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