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An SU(2n)-valued nonlinear Fourier transform
Michel Alexis, Lars Becker, Diogo Oliveira e Silva, Christoph Thiele·January 7, 2026
math.CAmath.FAQuantum Physics
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Abstract
We define a nonlinear Fourier transform which maps sequences of contractive $n \times n$ matrices to $SU(2n)$-valued functions on the circle $\mathbb{T}$. We characterize the image of finitely supported sequences and square-summable sequences on the half-line, and construct an inverse for $SU(2n)$-valued functions whose diagonal $n \times n$ blocks are outer matrix functions. As an application, we relate this nonlinear Fourier transform with quantum signal processing over $U(2n)$ and multivariate quantum signal processing.