Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Estimation Lie Algebra Associated with Quantum Filters   We introduce the Lie algebra of super-operators associated with a quantum
filter, specifically emerging from the Stratonovich calculus. In classical
filtering, the analogue algebra leads to a geometric theory of nonlinear
filtering which leads to well-known results by Brockett and by Mitter
characterizing potential models where the curse-of-dimensionality may be
avoided, and finite dimensional filters obtained. We discuss the quantum
analogue to these results. In particular, we see that, in the case where all
outputs are subjected to homodyne measurement, the Lie algebra of
super-operators is isomorphic to a Lie algebra of system operators from which
one may approach the question of the existence of finite-dimensional filters.

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The categories of this paper are: q-fin
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th