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.

翻译：在本篇文章中,我们证明冯纽曼双代数中各种顺利的不确定原则,这些原则统一了量衡对称的不确定原则数量,如分因数和在量子Fourier分析中研究的聚合双代数等。我们还为冯纽曼双代数获得了Widgerson-Wigderson型的不确定原则。此外,我们对A.Wigderson和Y.Wigderson提出的一个推测给出了完整的答案。