Complementary Jupyter notebooks to

The Mueller matrix cone and its application to filtering

The missing symbolic computations can be found in the Symbolic Jupyter Notebook. The implementation of the derived filters and its numerical application to some Mueller matrices can be found in the Numeric Jupyter Notebook.

Please cite:

    @article{Zander:20,
author = {Tim Zander and Juergen Beyerer},
journal = {OSA Continuum},
keywords = {Lie algebraic and group methods; Mueller matrices; Optical elements; Quantum information; Quantum optics; Quantum process tomography},
number = {6},
pages = {1376--1384},
publisher = {OSA},
title = {Mueller matrix cone and its application to filtering},
volume = {3},
month = {Jun},
year = {2020},
url = {http://www.osapublishing.org/osac/abstract.cfm?URI=osac-3-6-1376},
doi = {10.1364/OSAC.383317},
abstract = {We show that there is an isometry between the real ambient space of all Mueller matrices and the space of all Hermitian matrices that maps the Mueller matrices onto the positive semidefinite matrices. We use this to establish an optimality result for the filtering of Mueller matrices, which roughly says that it is always enough to filter the eigenvalues of the corresponding \&\#x201C;coherency matrix.\&\#x201D; Then we further explain how the knowledge of the cone of Hermitian positive semidefinite matrices can be transferred to the cone of Mueller matrices with a special emphasis towards optimisation. In particular, we suggest that means of Mueller matrices should be computed within the corresponding Riemannian geometry.},
}