Quantum Fourier Analysis

• URL: http://arxiv.org/abs/2002.03477v1
• Date: Mon, 10 Feb 2020 00:25:53 GMT
• Title: Quantum Fourier Analysis
• Authors: Arthur Jaffe, Chunlan Jiang, Zhengwei Liu, Yunxiang Ren, and Jinsong Wu
• Abstract summary: Quantum Fourier analysis is a new subject that combines an algebra with analytic estimates. This provides interesting tools to investigate phenomena such as quantum symmetry. We cite several applications of the quantum Fourier analysis in subfactor theory, in category theory, and in quantum information.
• Score: 1.776439648597615
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: {\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.

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