Preparation of maximally-entangled states with multiple cat-state qutrits in circuit QED

In recent years, cat-state encoding and high-dimensional entanglement have attracted much attention. However, previous works are limited to generation of entangled states of cat-state qubits (two-dimensional entanglement with cat-state encoding), while how to prepare entangled states of cat-state qutrits or qudits (high-dimensional entanglement with cat-state encoding) has not been investigated. We here propose to generate a maximally-entangled state of multiple cat-state qutrits (three-dimensional entanglement by cat-state encoding) in circuit QED. The entangled state is prepared with multiple microwave cavities coupled to a superconducting flux ququart (a four-level quantum system). This proposal operates essentially by the cavity-qutrit dispersive interaction. The circuit hardware resource is minimized because only a coupler ququart is employed. The higher intermediate level of the ququart is occupied only for a short time, thereby decoherence from this level is greatly suppressed during the state preparation. Remarkably, the state preparation time does not depend on the number of the qutrits, thus it does not increase with the number of the qutrits. As an example, our numerical simulations demonstrate that, with the present circuit QED technology, the high-fidelity preparation is feasible for a maximally-entangled state of two cat-state qutrits. Furthermore, we numerically analyze the effect of the inter-cavity crosstalk on the scalability of this proposal. This proposal is universal and can be extended to accomplish the same task with multiple microwave or optical cavities coupled to a natural or artificial four-level atom.