Quantum smooth uncertainty principles for von Neumann bi-algebras

2021/07/19 by Linzhe Huang, Zhengwei Liu, Huang, Linzhe +3 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Mathematical Analysis and Transform Methods #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2107.09057

Abstract

In this article, we prove various smooth uncertainty principles on von Neumann bi-algebras, which unify numbers of uncertainty principles on quantum symmetries, such as subfactors, and fusion bi-algebras etc, studied in quantum Fourier analysis. We also obtain Widgerson-Wigderson type uncertainty principles for von Neumann bi-algebras. Moreover, we give a complete answer to a conjecture proposed by A. Wigderson and Y. Wigderson.

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• Higher reflections and entropy of canonical shifts for inclusions of C^*-algebras with finite Watatani index

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