https://doi.org/10.1140/epjqt/s40507-015-0028-y
Research
On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs
1
Edward L. Ginzton Laboratory, Stanford University, Stanford, CA, 94305, USA
2
CNRS, Laboratoire des signaux et systèmes (L2S) CentraleSupélec, 3 rue Joliot-Curie, Gif-sur-Yvette, 91192, France
3
ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Australian National University, Canberra, ACT, 0200, Australia
* e-mail: nina.amini@lss.supelec.fr
Received:
26
December
2014
Accepted:
2
June
2015
Published online:
17
June
2015
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.
Key words: linear quantum stochastic differential equations (QSDEs) / quantum noises / Kalman filtering / physical realizability / linear least mean squares estimators / non-commutative outputs / coherent observers
© Amini et al., 2015
