Measurement-Based Control of Quantum Entanglement and Steering in a Distant Magnomechanical System

In this paper, we propose a scheme for measurement-based control of hybrid Einstein-Podolsky-Rosen (EPR) entanglement and steering between distant macroscopic mechanical oscillator and yttrium iron garnet (YIG) sphere in a system of an electromechanical cavity unidirectionally coupled to an electromagnonical cavity. We reveal that when the output of the electromagnonical cavity is continuously monitored by homodyne detection, not only the phonon-magnon entanglement and steering but also the purities of the phononic, magnonic and phonon-magnon states are considerably enhanced. We also find that the measurement can effectively retrieve the magnon-to-phonon steering, which is not yet obtained in the absence of the measurement. We show that unconditional phonon-magnon entanglement and steering can be achieved by introducing indirect feedback to drive the magnon and mechanical subsystems. The long-distance macroscopic hybrid entanglement and steering can be useful for, e.g., fundamental tests for quantum mechanics and quantum networks.