Simple factorization of unitary transformations
Hubert de Guise, Olivia Di Matteo, Luis Lorenzo Sánchez-Soto · Physical Review A · 2018
We demonstrate a method for general linear optical networks that allows one to factorize any $\mathrm{SU}(n$) matrix in terms of two $\mathrm{SU}(n\ensuremath{-}1)$ blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in a straightforward way, ending in a tidy arrangement of SU(2) transformations. The method hinges only on a linear relationship between input and output states, and can thus be applied to a variety of scenarios, such as microwaves, acoustics, and quantum fields.