W. K. Yam, S. Gandorfer, F. Fesquet, M. Handschuh, K. E. Honasoge, A. Marx, R. Gross, K. G. Fedorov

Quantum communication in the microwave regime is set to play an important role in distributed quantum computing and hybrid quantum networks. However, typical superconducting quantum circuits require millikelvin temperatures for operation, which poses a significant challenge for largescale microwave quantum networks. Here, we present a solution to this challenge by demonstrating the successful quantum teleportation of microwave coherent states between two spatially-separated dilution refrigerators over a thermal microwave channel with a temperature of $4$ K. We distribute two-mode squeezed states over the noisy channel and employ the resulting quantum entanglement for quantum teleportation of coherent states with fidelities of $72.3 \pm 0.5 ~\%$ at $1$ K and $59.9 \pm 2.5 ~\%$ at $4$ K, exceeding the no-cloning and classical communication thresholds, respectively. We successfully model the teleportation protocol using a Gaussian operator formalism that includes losses and noise. This analysis shows that the teleportation infidelity mainly stems from a parasitic heating of the cold quantum nodes due to the hot network connection. Our results prove the experimental feasibility of distributed superconducting architectures and motivate practical applications of noisy quantum networks in various frequency regimes.