We study creation of entanglement and quantum steering in a parity-time- ($\mathcal{PT}$-) symmetric cavity magnomechanical system. There are photon–magnon coupling and phonon–magnon coupling in this system. By introducing a gain cavity mode, a $\mathcal{PT}$-symmetric Hamiltonian of the system is obtained. We find that bipartite entanglement and magnon$\to$phonon steering in $\mathcal{PT}$-symmetry system (gain–loss system) are significantly enhanced versus the case in the conventional cavity magnomechanical system (loss–loss system). Moreover, the magnon$\to$phonon one-way-like quantum steering can be realized in unbroken-$\mathcal{PT}$-symmetry regime. The boundary of stability is demonstrated and it shows that the gain–loss system becomes more stable with respect to the conventional loss–loss system under the parameters we consider. This work opens up a route to explore the characteristics of quantum entanglement and steering in magnomechanical systems, which might have potential applications in quantum state engineering and quantum information.

我们研究奇偶时间内纠缠和量子控制的产生-（$\mathcal{PT}$-）对称腔的机械系统。该系统中有光子-磁振子耦合和声子-磁振子耦合。通过引入增益腔模式，$\mathcal{PT}$得到系统的对称哈密顿量。我们发现二分纠缠和磁振子$\to$声子转向 $\mathcal{PT}$-对称系统（增益-损耗系统）与常规腔体诊断机械系统（损耗-损耗系统）相比得到了显着增强。而且，马农$\to$声子单向量子转向可以不间断地实现，$\mathcal{PT}$对称体制。证明了稳定性的边界，它表明在我们考虑的参数下，损益系统相对于常规损益系统变得更加稳定。这项工作为探索机械系统中量子纠缠和操纵的特性开辟了一条途径，这可能在量子态工程和量子信息中具有潜在的应用。