In distributed functional monitoring (DFM), N players located at different sites; each observes a stream of items and communicates with one coordinator, whose goal is to compute a function of the union of the streams. In threshold monitoring, a special case of DFM, the coordinator wants to know whether f(v(t)) > T, where v(t) is a binary vector that represents the state of the stream as an average of local states at the sites. In this paper, we enhance the classical geometric monitoring (GM) method with quantum communication and entanglement. The proposed quantum geometric monitoring (QGM) protocol can be further specialized by defining specific network topologies. In QGM-Flat, the coordinator is connected to all N players. When N becomes too large, the performance of QGM-Flat deteriorates. For a scalable implementation, we propose to organize the players in a tree structure, with the QGM-Tree protocol. We have implemented both QGM-Flat and QGM-Tree with SimulaQron, a novel Python library for the development and simulation of quantum networking applications. We analyze the proposed quantum protocols, showing that they outperform their classical counterparts in terms of reduced communication cost, while showing the same accuracy.
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