In this paper we recast the Serret theorem about a characterization of palindromic continued fractions in the context of polynomial continued fractions. Then, using the relation between symmetric tridiagonal matrices and polynomial continued fractions we give a quick exposition of the mathematical aspect of the perfect quantum state transfer problem.

中文翻译：

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Joseph-Alfred Serret的一个定理及其与完美量子态转移的关系

在本文中，我们重塑了有关多项式连续分数背景下回文连续分数特征的Serret定理。然后，利用对称三对角矩阵与多项式连续分数之间的关系，我们给出了完美量子态转移问题的数学方面的快速解释。