Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Loss of Memory and Convergence of Quantum Markov Processes   In a quantum (inhomogeneous) Markov process $\rho_1:=\Gamma_1(\rho)$,
$\rho_2:=\Gamma_1(\rho_1)$, ..., where $\Gamma_i$ are CPTP maps and $\rho$ is
the initial state, the the state of the system is either oscillatory or
convergent to a point or convergent to an oscillatory orbit. Whichever the case
it is, "information" about the initial state is always monotone non-increasing
and convergent. This fact motivate us to define an equivalence class of
families of quantum states, which embodies the bundle of all "information
quantities" about the initial state. We show, for any quantum inhomogeneous
Markov process over a finite dimensional Hilbert space, the trajectory in the
space of the all equivalence classes is "monotone decreasing" and convergent to
a point, relative to a reasonablly defined topology. Also, a characterization
of weak ergodicity in this picture is given.

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The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
2
The categories of this paper are: math
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph