  Recently, consensus-type problems have been formulated in the quantum domain.
Obtaining average quantum consensus consists in the dynamical symmetrization of
a multipartite quantum system while preserving the expectation of a given
global observable. In this paper, two improved ways of obtaining consensus via
dissipative engineering are introduced, which employ on quasi local preparation
of mixtures of symmetric pure states, and show better performance in terms of
purity dynamics with respect to existing algorithms. In addition, the first
method can be used in combination with simple control resources in order to
engineer pure Dicke states, while the second method guarantees a stronger type
of consensus, namely single-measurement consensus. This implies that outcomes
of local measurements on different subsystems are perfectly correlated when
consensus is achieved. Both dynamics can be randomized and are suitable for
feedback implementation.
