Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum filtering for multiple diffusive and Poissonian measurements   We provide a rigorous derivation of a quantum filter for the case of multiple
measurements being made on a quantum system. We consider a class of measurement
processes which are functions of bosonic field operators, including
combinations of diffusive and Poissonian processes. This covers the standard
cases from quantum optics, where homodyne detection may be described as a
diffusive process and photon counting may be described as a Poissonian process.
We obtain a necessary and sufficient condition for any pair of such
measurements taken at different output channels to satisfy a commutation
relationship. Then, we derive a general, multiple measurement quantum filter as
an extension of a single-measurement quantum filter. As an application we
explicitly obtain the quantum filter corresponding to homodyne detection and
photon counting at the output ports of a beam splitter, correcting an earlier
result.

26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin