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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 generalizations of classical consensus states. This new viewpoint can be directly used to study consensus for probability distributions, as these can be seen as a particular case of quantum statistical states: in this light, our analysis is also relevant for classical problems. We then extend the gossip consensus algorithm to the quantum setting and prove it converges to symmetric states while preserving the expectation of permutation-invariant global observables. Applications of the framework and the algorithms to estimation and control problems on quantum networks are discussed.

Raw measurement data are too noisy to directly obtain queue and traffic flow estimates usable for feedback control of urban traffic. In this paper, we propose a recursive filter to estimate traffic state by combining the real-time measurements with a reduced model of expected traffic behavior. The latter is based on platoons rather than individual vehicles in order to achieve faster implementations. This new model is used as a predictor for real-time traffic estimation using the particle filtering framework. As it becomes infeasible to let a truly large traffic network be managed by one central computer, with which all the local units would have to communicate, we also propose a distributed version of the particle filter (PF) where the local estimators exchange information on flows at their common boundaries. We assess the quality of our platoon-based PFs, both centralized and distributed, by comparing their queue-size estimates with the true queue sizes in simulated data.