Figure 3

The magnon-magnon entanglement \(E_{N}^{m_{1}m_{2}}\), quantum steering \(\mathcal{G}_{1\rightarrow 2}\) and \(\mathcal{G}_{2\rightarrow 1}\), steering asymmetry \(\mathcal{G}_{as}\) and populations of magnon modes versus \(\kappa _{2}/\kappa _{1}\) for \(g_{1}=g_{2}\) in (a,c), and versus \(g_{2}/g_{1}\) for \(\kappa _{2}/2\pi = 1.5\kappa _{1}/2\pi = 6\text{ MHz}\) in (b,d). The cavity detuning and magnon detuning satisfy the relation \(\Delta _{1}=\Delta _{a}\) (\(\Delta _{2}=-\Delta _{a}\)), and the other parameters are the same as in Fig. 2