Generation of Greenberger-Horne-Zeilinger entangled states of photons in multiple cavities via a superconducting qutrit or an atom through resonant interaction

We propose an efficient method to generate a Greenberger-Horne-Zeilinger entangled state of n photons in n microwave cavities (or resonators) via resonant interaction to a single superconducting qutrit. The deployment of a qutrit, instead of a qubit, as the coupler enables us to use resonant interactions exclusively for all qutrit-cavity and qutrit-pulse operations. This unique approach significantly shortens the time of operation, which is advantageous for reducing the adverse effects of qutrit decoherence and cavity decay on the fidelity of the protocol. Furthermore, the protocol involves no measurement on either the state of the qutrit or cavity photons. We also show that the protocol can be generalized to other systems by replacing the superconducting qutrit coupler with different types of physical qutrits, such as an atom in the case of cavity QED, to accomplish the same task.