Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General fixed points of quasi-local frustration-free quantum semigroups:
  from invariance to stabilization   We investigate under which conditions a mixed state on a finite-dimensional
multipartite quantum system may be the unique, globally stable fixed point of
frustration-free semigroup dynamics subject to specified quasi-locality
constraints. Our central result is a linear-algebraic necessary and sufficient
condition for a generic (full-rank) target state to be frustration-free
quasi-locally stabilizable, along with an explicit procedure for constructing
Markovian dynamics that achieve stabilization. If the target state is not
full-rank, we establish sufficiency under an additional condition, which is
naturally motivated by consistency with pure-state stabilization results yet
provably not necessary in general. Several applications are discussed, of
relevance to both dissipative quantum engineering and information processing,
and non-equilibrium quantum statistical mechanics. In particular, we show that
a large class of graph product states (including arbitrary thermal graph
states) as well as Gibbs states of commuting Hamiltonians are frustration-free
stabilizable relative to natural quasi-locality constraints. Likewise, we
provide explicit examples of non-commuting Gibbs states and non-trivially
entangled mixed states that are stabilizable despite the lack of an underlying
commuting structure, albeit scalability to arbitrary system size remains in
this case an open question.

17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
16
The categories of this paper are: stat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con