论文标题
量子傅里叶分析
Quantum Fourier Analysis
论文作者
论文摘要
{\ em量子傅里叶分析}是一个新主题，它结合了代数傅立叶变换（在亚比例理论的情况下）与分析估计。这为研究现象（例如量子对称性）提供了有趣的工具。我们在量子傅里叶变换$ \ fs $上建立界限，作为适当定义的$ l^{p} $空间之间的地图，从而导致了相对熵的新不确定性原理。我们在亚比例理论，类别理论和量子信息中引用了量子傅立叶分析的几个应用。我们建议新的拓扑不平等，并概述了几个开放问题。
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum symmetry. We establish bounds on the quantum Fourier transform $\FS$, as a map between suitably defined $L^{p}$ spaces, leading to a new uncertainty principle for relative entropy. We cite several applications of the quantum Fourier analysis in subfactor theory, in category theory, and in quantum information. We suggest a new topological inequality, and we outline several open problems.
