Quantum Fourier analysis

Arthur Jaffe Harvard University, Cambridge, MA Chunlan Jiang Department of Mathematics, Hebei Normal University, Shijiazhuang, Hebei Zhengwei Liu Yau MathematicalScience Center, Tsinghua University, Beijing Yunxiang Ren Department of Mathematics, Tsinghua University, Beijing Jinsong Wu Institute forAdvanced Study in Mathematics, Harbin Institute of Technology, Harbin

TBD mathscidoc:2203.43022

Proceedings of the National Academy of Sciences of the United States of America, 117, (20), 10715-10720, 2020.5
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 L^p 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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@inproceedings{arthur2020quantum,
  title={Quantum Fourier analysis},
  author={Arthur Jaffe, Chunlan Jiang, Zhengwei Liu, Yunxiang Ren, and Jinsong Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220316101046699545969},
  booktitle={Proceedings of the National Academy of Sciences of the United States of America},
  volume={117},
  number={20},
  pages={10715-10720},
  year={2020},
}
Arthur Jaffe, Chunlan Jiang, Zhengwei Liu, Yunxiang Ren, and Jinsong Wu. Quantum Fourier analysis. 2020. Vol. 117. In Proceedings of the National Academy of Sciences of the United States of America. pp.10715-10720. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220316101046699545969.
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