Conjectured $DXZ$ decompositions of a unitary matrix

• URL: http://arxiv.org/abs/2112.00226v1
• Date: Wed, 1 Dec 2021 01:59:15 GMT
• Title: Conjectured $DXZ$ decompositions of a unitary matrix
• Authors: Alexis De Vos, Martin Idel, Stijn De Baerdemacker
• Abstract summary: We conjecture that these two decompositions are merely special cases of a set of decompositions. For lack of a proof, we provide an iterative Sinkhorn algorithm to find an approximate numerical decomposition.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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