Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heisenberg Picture Approach to the Stability of Quantum Markov Systems   Quantum Markovian systems, modeled as unitary dilations in the quantum
stochastic calculus of Hudson and Parthasarathy, have become standard in
current quantum technological applications. This paper investigates the
stability theory of such systems. Lyapunov-type conditions in the Heisenberg
picture are derived in order to stabilize the evolution of system operators as
well as the underlying dynamics of the quantum states. In particular, using the
quantum Markov semigroup associated with this quantum stochastic differential
equation, we derive sufficient conditions for the existence and stability of a
unique and faithful invariant quantum state. Furthermore, this paper proves the
quantum invariance principle, which extends the LaSalle invariance principle to
quantum systems in the Heisenberg picture. These results are formulated in
terms of algebraic constraints suitable for engineering quantum systems that
are used in coherent feedback networks.

35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph