Quantum Fourier analysis
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Updated: Dec 22, 2025

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans
Published on: September 13, 2017
Arthur Jaffe1, Chunlan Jiang2, Zhengwei Liu3,4
1Harvard University, Cambridge, MA 02138; jaffe@g.harvard.edu liuzhengwei@mail.tsinghua.edu.cn.
Abstract:
Quantum Fourier analysis is a 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 F, as a map between suitably defined [Formula: see text] spaces, leading to an uncertainty principle for relative entropy. We cite several applications of quantum Fourier analysis in subfactor theory, in category theory, and in quantum information. We suggest a topological inequality, and we outline several open problems.
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