Generation of high-fidelity Greenberger-Horne-Zeilinger states in a driven hybrid quantum system

In this study, we propose a theoretical scheme for achieving long-distance Greenberger-Horne-Zeilinger states in a driven hybrid quantum system. By applying a microwave field to the YIG sphere, we utilize the Kerr effect to induce the squeezing of the magnon, thereby achieving an exponential enhancement of the coupling strength between the magnonic mode and spins, and we also discuss in detail the relationship between the squeezing parameter and the external microwave field. By means of the Schrieffer-Wolff transformation, the magnonic mode can be adiabatically eliminated under the large detuning condition, thereby establishing a robust effective interaction between spins essential for realizing the desired entangled state. Numerical simulations indicate that the squeezing parameter can be effectively increased by adjusting the driving field, and our proposal can generate high-fidelity Greenberger-Horne-Zeilinger states even in dissipative systems. Additionally, we extensively discuss the influence of inhomogeneous broadening on the entangled states, and the experimental feasibility shows that our results provide possibilities in the realms of quantum networking and quantum computing.