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Mutually Unbiased Property of Special Entangled Bases

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Abstract

We study mutually unbiased bases formed by special entangled basis with fixed Schmidt number 2 (MUSEB2s) in \(\mathbb {C}^{3}\otimes \mathbb {C}^{4p} (p\in \mathbb {Z}^{+})\). Through analyzing the conditions MUSEB2s satisfy, a systematic way of the concrete construction of MUSEB2s in \(\mathbb {C}^{3}\otimes \mathbb {C}^{4p}\) is established. A general approach to constructing MUSMEB2s in \(\mathbb {C}^{3}\otimes \mathbb {C}^{4p}(p\in \mathbb {Z}^{+})\) from MUSMEB2s in \(\mathbb {C}^{3}\otimes \mathbb {C}^{4}\) is also presented. Detailed examples in \(\mathbb {C}^{3}\otimes \mathbb {C}^{4}\), \(\mathbb {C}^{3}\otimes \mathbb {C}^{8}\) and \(\mathbb {C}^{3}\otimes \mathbb {C}^{12}\) are given. Especially, by choosing special entangled basis with fixed Schmidt number 2 (SEB2) from [J. Phys. A. Math. Theor. 48245301(2015)], the limitation of \(3\nmid p\) in [Quantum Inf. Process. 17:58(2018)] is successfully deleted.

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Acknowledgements

This work is supported by National Natural Science Foundation of China under number 11761073, 11901163.

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Authors and Affiliations

  1. Department of Big Data, School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023, China

    Yuan-Hong Tao, Shu-Hui Wu & Cai-Hong Wang

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

    Yuan-Hong Tao, Xin-Lei Yong & Yi-Fan Han

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  1. Yuan-Hong Tao
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  2. Xin-Lei Yong
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  4. Shu-Hui Wu
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  5. Cai-Hong Wang
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Y. H. Tao and S. H. Wu wrote the main manuscript text. All of the authors reviewed the manuscript.

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Correspondence to Shu-Hui Wu.

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Tao, YH., Yong, XL., Han, YF. et al. Mutually Unbiased Property of Special Entangled Bases. Int J Theor Phys 60, 2653–2661 (2021). https://doi.org/10.1007/s10773-021-04840-x

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