Abstract
A collection \(\mathfrak {B}=\{B_1,B_2, \cdots , B_N\}\) of orthonormal bases of \(\mathbb {C}^K\) is called mutually unbiased bases if \(|\langle v_i|v_j\rangle |=\frac{1}{\sqrt{K}}\) for all \(v_i\in B_i\), \(v_j\in B_j\) and \(1\le i<j\le N\). In this paper, we present several new series of mutually unbiased bases constructed by utilizing p-ary weakly regular bent functions, permutation polynomials and PN functions over finite fields. Specifically, we are the first to use weakly regular bent functions to construct MUBs. In addition, we obtain a complete set of MUBs by employing linearized permutation polynomials over finite fields.
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This research is supported by the National Natural Science Foundation of China under Grant 12171241 and Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant KYCX21_0175.
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Qian, L., Cao, X. Several new constructions of mutually unbiased bases derived from functions over finite fields. Quantum Inf Process 21, 296 (2022). https://doi.org/10.1007/s11128-022-03636-0
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DOI: https://doi.org/10.1007/s11128-022-03636-0