On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs
Mathematical Physics
2015-06-23 v3 math.MP
Optimization and Control
Quantum Physics
Abstract
The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice.
Keywords
Cite
@article{arxiv.1406.4599,
title = {On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs},
author = {Nina H. Amini and Zibo Miao and Yu Pan and Matthew R. James and Hideo Mabuchi},
journal= {arXiv preprint arXiv:1406.4599},
year = {2015}
}
Comments
31 pages