Simple factorization of unitary transformations

de Guise, Hubert; Di Matteo, Olivia; Sanchez-Soto, Luis

doi:10.1103/PhysRevA.97.022328

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Simple factorization of unitary transformations

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Sanchez-Soto, Luis
Quantumness, Tomography, Entanglement, and Codes, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Citation

de Guise, H., Di Matteo, O., & Sanchez-Soto, L. (2018). Simple factorization of unitary transformations. Phys. Rev. A, 97, 022328. doi:10.1103/PhysRevA.97.022328.

Cite as: https://hdl.handle.net/21.11116/0000-0002-985B-D

Abstract

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.