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Approximately Mutually Unbiased Bases by Frobenius Rings

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Abstract

A collection \(\beta = \left\{ {{B_1},{B_2}, \cdots \,,{B_N}} \right\}\) of orthonormal bases for ℂL is called approximately mutually unbiased bases if \(\left| {\left\langle {u,u} \right\rangle } \right| \leqslant \tfrac{1}{{\sqrt L }}\left( {1 + o\left( 1 \right)} \right)\) for all u ∈ Bi, v ∈ Bj and 1 ≤ i ≤ j ≤ N. In this paper, the authors construct approximately mutually unbiased bases by using Gauss sums over Frobenius rings.

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Acknowledgements

This work grows out of the first author’s master thesis at Chulalongkorn University written under the direction of the second author to whom she expresses her gratitude. The first author was supported in part by the Human Resource Development in Science Project (Science Achievement Scholarship of Thailand, SAST).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand

    Naparat Sripaisan & Yotsanan Meemark

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  1. Naparat Sripaisan
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  2. Yotsanan Meemark
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Correspondence to Yotsanan Meemark.

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This paper was recommended for publication by Editor DENG Yingpu.

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Sripaisan, N., Meemark, Y. Approximately Mutually Unbiased Bases by Frobenius Rings. J Syst Sci Complex 33, 1244–1251 (2020). https://doi.org/10.1007/s11424-020-8251-8

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  • DOI: https://doi.org/10.1007/s11424-020-8251-8

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