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arXiv · 2112.00226

Conjectured $DXZ$ decompositions of a unitary matrix

Alexis De Vos·Martin Idel·Stijn De Baerdemacker
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Abstract

For any unitary matrix there exists a ZXZ decomposition, according to a theorem by Idel and Wolf. For any even-dimensional unitary matrix there exists a block-ZXZ decomposition, according to a theorem by F\"uhr and Rzeszotnik. We conjecture that these two decompositions are merely special cases of a set of decompositions, one for every divisor of the matrix dimension. For lack of a proof, we provide an iterative Sinkhorn algorithm to find an approximate numerical decomposition.

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Alexis De Vos, Martin Idel, Stijn De Baerdemacker. 2021-12-01. Conjectured $DXZ$ decompositions of a unitary matrix. https://arxiv.org/abs/2112.00226

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