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The human brain acts as a very efficient parallel classical-quantum communications system relating responses to a multitude of input signals from sensors. However, the mechanisms of the quantum communication channel in the brain remain a mystery. Since matter and energy cannot be teleported, in the sense of transferring from one place to another without passing through intermediate locations, teleportation of quantum states, as the ultimate structure of objects, is possible. Only the structure, information about conformation state, is teleported - the matter stays at the source side and has to be already present at the final location. From this point of view, we consider a new type of network in the brain, based on a unity of classical and quantum neural-astrocyte networks. Matter and energy (classical channel) and classical quantum information travel through neurons, while through the astrocyte-neuron loop travel classical quantum and non-classical quantum information. The new type of network is a synergetic one with quite new energy-information properties compared to classical neuron networks.