Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reaching a Quantum Consensus: Master Equations that Generate
  Symmetrization and Synchronization   In this paper, we propose and study a master-equation based approach to drive
a quantum network with $n$ qubits to a consensus (symmetric) state introduced
by Mazzarella et al. The state evolution of the quantum network is described by
a Lindblad master equation with the Lindblad terms generated by continuous-time
swapping operators, which also introduce an underlying interaction graph. We
establish a graphical method that bridges the proposed quantum consensus scheme
and classical consensus dynamics by studying an induced graph (with $2^{2n}$
nodes) of the quantum interaction graph (with $n$ qubits). A fundamental
connection is then shown that quantum consensus over the quantum graph is
equivalent to componentwise classical consensus over the induced graph, which
allows various existing works on classical consensus to be applicable to the
quantum setting. Some basic scaling and structural properties of the quantum
induced graph are established via combinatorial analysis. Necessary and
sufficient conditions for exponential and asymptotic quantum consensus are
obtained, respectively, for switching quantum interaction graphs. As a quantum
analogue of classical synchronization of coupled oscillators, quantum
synchronization conditions are also presented, in which the reduced states of
all qubits tend to a common trajectory.

32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg