A comparative study of estimation methods in quantum tomography
Abstract
As quantum tomography is becoming a key component of the quantum engineering toolbox, there is a need for a deeper understanding of the multitude of estimation methods available. Here we investigate and compare several such methods: maximum likelihood, least squares, generalised least squares, positive least squares, thresholded least squares and projected least squares. The common thread of the analysis is that each estimator projects the measurement data onto a parameter space with respect to a specific metric, thus allowing us to study the relationships between different estimators.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 June 2019
 DOI:
 10.1088/17518121/ab1958
 arXiv:
 arXiv:1901.07991
 Bibcode:
 2019JPhA...52w4001A
 Keywords:

 quantum tomography;
 statistical methods;
 maximum likelihood;
 least squares tomography;
 projected least squares;
 low rank states;
 Quantum Physics;
 Mathematical Physics;
 Mathematics  Statistics Theory
 EPrint:
 40 pages, 11 figures