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We demonstrate a method for general linear optical networks that allows one to factorize any SU (n) matrix in terms of two SU (n-1) blocks coupled by an SU (2) entangling beam splitter. The process can be recursively continued in an efficient 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.
Guise et al. (Tue,) studied this question.