Magnon-magnon entanglement and its quantification via a microwave cavity

Quantum magnonics is an emerging research field, with great potential for applications in magnon based hybrid systems and quantum information processing. Quantum correlation, such as entanglement, is a central resource in many quantum information protocols that naturally comes about in any study toward quantum technologies. This applies also to quantum magnonics. Here, we investigate antiferromagnetic coupling of two ferromagnetic sublattices that can have two different magnon modes. We show how this may lead to experimentally measurable bipartite continuous-variable magnon-magnon entanglement. The entanglement can be fully characterized via a single squeezing parameter or, equivalently, entanglement parameter. The clear relation between the entanglement parameter and the Einstein, Podolsky, and Rosen (EPR) function of the ground state opens up for experimental quantification magnon-magnon continuous-variable entanglement and EPR nonlocality. We propose a practical experimental realization to measure the EPR function of the ground state, in a setting that relies on magnon-photon interaction in a microwave cavity.