Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Preservation of Commutation Relations and Physical Realizability of Open
  Two-Level Quantum Systems   Coherent feedback control considers purely quantum controllers in order to
overcome disadvantages such as the acquisition of suitable quantum information,
quantum error correction, etc. These approaches lack a systematic
characterization of quantum realizability. Recently, a condition characterizing
when a system described as a linear stochastic differential equation is quantum
was developed. Such condition was named physical realizability, and it was
developed for linear quantum systems satisfying the quantum harmonic oscillator
canonical commutation relations. In this context, open two-level quantum
systems escape the realm of the current known condition. When compared to
linear quantum system, the challenges in obtaining such condition for such
systems radicate in that the evolution equation is now a bilinear quantum
stochastic differential equation and that the commutation relations for such
systems are dependent on the system variables. The goal of this paper is to
provide a necessary and sufficient condition for the preservation of the Pauli
commutation relations, as well as to make explicit the relationship between
this condition and physical realizability.

27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: funct-an
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph