Cost and Routing of Continuous Variable Quantum Networks

We study continuous-variable graph states with regular and complex network shapes 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 provide an analytical formula to compute the experimental resources required to implement the graph states and we use it to show that the scaling of the squeezing cost with the size of the network strictly depends on its topology. We show that homodyne measurements along parallel paths between two nodes allow to increase the final entanglement in these nodes and we use this effect to boost the efficiency of an entanglement routing protocol. The devised routing protocol is particularly efficient in running-time for complex sparse networks.