Conjectured $DXZ$ decompositions of a unitary matrix
Quantum Physics
2021-12-02 v1
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.
Keywords
Cite
@article{arxiv.2112.00226,
title = {Conjectured $DXZ$ decompositions of a unitary matrix},
author = {Alexis De Vos and Martin Idel and Stijn De Baerdemacker},
journal= {arXiv preprint arXiv:2112.00226},
year = {2021}
}