Generation of a bipartite mechanical cat state by performing projective Bell-state measurement on a pair of superconducting qubits

Quantum state preparation and measurement of photonic and phononic Schr"odinger cat states have gathered significant interest due to their implications for alternative encoding schemes in quantum computation. These schemes employ coherent state superpositions, leveraging the expanded Hilbert space provided by cavity or mechanical resonators in contrast to two-level systems. Moreover, such cat states also serve as a platform for testing fundamental quantum phenomena in macroscopic systems. In this study, we generate four bipartite phononic cat states using an entanglement swapping scheme achieved through projective Bell-state measurements on two superconducting qubits. Employing two superconducting qubits allows for the creation of bipartite phononic cat states remotely, where the two phononic resonators are separated by a far distance. Subsequently, we conduct a Bell inequality test on the bipartite cat state using the Clauser-Horne-Shimony-Holt formulation. Given that the entangled cat states are generated through entanglement swapping, our approach holds promising applications for the advancement of complex quantum network processors based on continuous-variable systems.