  This paper extends the consensus framework, widely studied in the literature
on distributed computing and control algorithms, to networks of quantum
systems. We define consensus situations on the basis of invariance and symmetry
properties, finding four different probabilistic generalizations of classical
consensus states. We then extend the gossip consensus algorithm to the quantum
setting and prove its convergence properties, showing how it converges to
symmetric states while preserving the expectation of permutation-invariant
global observables.
