### Abstract

We study continuous-variable graph states as quantum communication networks. We explore graphs with regular and complex network shapes distributed among different agents and we report for their cost as a global measure of squeezing and number of squeezed modes that are necessary to build the network. We show that the trend of the squeezing cost presents a non-trivial scaling with the size of the network strictly dependent on its topology. We devise a routing protocol based on local quadrature measurements for reshaping the network in order to perform teleportation protocol between two arbitrary nodes of the networks. The \textit{Routing} protocol, which is based on wire-shortening over parallel paths among the nodes, improves the final entanglement between the two nodes in a considerable amount of cases, and it is particularly efficient in running-time for complex sparse networks.

Publication

Cost and Routing of Continuous Variable Quantum Networks

We study continuous-variable graph states as quantum communication networks. We explore graphs with regular and complex network shapes distributed among different agents and we report for their cost as a global measure of squeezing and number of squeezed modes that are necessary to build the network. We show that the trend of the squeezing cost presents a non-trivial scaling with the size of the network strictly dependent on its topology. We devise a routing protocol based on local quadrature measurements for reshaping the network in order to perform teleportation protocol between two arbitrary nodes of the networks. The \textit{Routing} protocol, which is based on wire-shortening over parallel paths among the nodes, improves the final entanglement between the two nodes in a considerable amount of cases, and it is particularly efficient in running-time for complex sparse networks.