Multipartite EPR-steering and entanglement in a cavity magnomechanical system through coherent feedback

Multipartite Einstein-Podolsky-Rosen (EPR) steering plays a crucial role in realizing secure quantum communication. In this paper, we theoretically investigate bipartite and tripartite quantum correlations, including entanglement and Gaussian quantum steering, in a cavity magnomechanical system incorporating a coherent feedback loop. We quantify and compare entanglement and Gaussian steering for four coupled bipartite Gaussian modes. Our results show that tuning the beam splitter's reflectivity parameter significantly enhances entanglement in both bipartite and tripartite states. Furthermore, we verify Coffman-Kundu-Wootters (CKW)-type monogamy inequalities for Gaussian steering among three tripartite modes for specific reflectivity values, and reveal the presence of one-way steering. These findings validate our system and demonstrate its potential for robust detection of multipartite entanglement and steering.