A collection \(\beta = \left\{ {{B_1},{B_2}, \cdots \,,{B_N}} \right\}\) of orthonormal bases for ℂ^L 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 ∈ B_i, v ∈ B_j and 1 ≤ i ≤ j ≤ N. In this paper, the authors construct approximately mutually unbiased bases by using Gauss sums over Frobenius rings.

中文翻译：

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Frobenius环的近似互不偏基

\ ^L的正交范数的集合\（\ beta = \ left \ {{{B_1}，{B_2}，\ cdots \，{B_N}} \ right \} \）被称为近似互不偏基，如果\（ \ left | {\ left \ langle {u，u} \ right \ rangle} \ right | \ leqslant \ tfrac {1} {{\ sqrt L}} \ left（{1 + o \ left（1 \ right）} \右）\）对于所有ü ∈乙_我，v ∈乙_Ĵ和1≤我≤ Ĵ ≤ ñ。在本文中，作者使用Frobenius环上的高斯和构造了近似互不偏的基。