Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum walks in the density operator picture   A new approach to quantum walks is presented. Considering a quantum system
undergoing some unitary discrete-time evolution in a directed graph G, we think
of the vertices of G as sites that are occupied by the quantum system, whose
internal state is described by density operators. To formulate the unitary
evolution, we define reflections in the tensor product of an internal Hilbert
space and a spatial Hilbert space. We then construct unitary channels that
govern the evolution of the system in the graph. The discrete dynamics of the
system (called quantum walks) is obtained by iterating the unitary channel on
the density operator of the quantum system. It turns out that in this
framework, the action of the unitary channel on a density operator is described
by the usual matrix multiplication.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph