Quantum Fourier analysis

Author:

Jaffe Arthur,Jiang Chunlan,Liu ZhengweiORCID,Ren YunxiangORCID,Wu Jinsong

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 Lp 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.

Funder

Templeton Religion Trust

DOD | United States Army | RDECOM | Army Research Office

National Natural Science Foundation of China

Tsinghua University

Publisher

Proceedings of the National Academy of Sciences

Subject

Multidisciplinary

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