Abstract
In this article, we prove various smooth uncertainty principles on von Neumann bi-algebras, which unify a number of uncertainty principles on quantum symmetries, such as subfactors, fusion bialgebras, etc., studied in quantum Fourier analysis. We also obtain Wigderson–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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