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Two Types of Maximally Entangled Bases and Their Mutually Unbiased Property in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime }}\)

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Abstract

We first construct a new maximally entangled basis in bipartite systems \(\mathbb {C}^{d} \otimes \mathbb {C}^{kd}\ (k\in Z^{+})\) which is diffrent from the one in Tao et al. (Quantum Inf. Process. 14, 2291 (2015)), then we generalize such maximally entangled basis into arbitrary bipartite systems \(\mathbb {C}^{d} \otimes \mathbb {C}^{d^{\prime }}\). We also study the mutual unbiased property of the two types of maximally entangled bases in bipartite systems \(\mathbb {C}^{d} \otimes \mathbb {C}^{kd}\). In particular, explicit examples in \(\mathbb {C}^{2} \otimes \mathbb {C}^{4}\), \(\mathbb {C}^{2} \otimes \mathbb {C}^{8}\) and \(\mathbb {C}^{3} \otimes \mathbb {C}^{3}\) are presented.

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Acknowledgments

This work is supported by Natural Science Foundation of China under number 11361065,11371114.

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Authors and Affiliations

  1. College of Mathematics, Zhengjiang University, Hangzhou, 310018, China

    Laizhen Luo

  2. College of Applied Mathematics, Harbin University of Science Technology, Harbin, 150080, China

    Laizhen Luo

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

    Xiaoyu Li & Yuanhong Tao

  4. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Yuanhong Tao

Authors
  1. Laizhen Luo
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  2. Xiaoyu Li
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  3. Yuanhong Tao
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Correspondence to Yuanhong Tao.

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Luo, L., Li, X. & Tao, Y. Two Types of Maximally Entangled Bases and Their Mutually Unbiased Property in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime }}\) . Int J Theor Phys 55, 5069–5076 (2016). https://doi.org/10.1007/s10773-016-3128-2

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  • DOI: https://doi.org/10.1007/s10773-016-3128-2

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