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arXiv · 1406.4599

On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

Nina H. Amini·Zibo Miao·Yu Pan·Matthew R. James·Hideo Mabuchi
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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.

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Nina H. Amini, Zibo Miao, Yu Pan, Matthew R. James, Hideo Mabuchi. 2014-06-18. On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs. https://arxiv.org/abs/1406.4599

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