Quantifying Entanglement by Purity in a Cavity-Magnon System

We study the realization and transfer of entanglement in a cavity-magnon system consisting of two cavities positioned at different locations, each containing a microwave (MW) field mode and a magnon mode of the yttrium iron garnet (YIG) sphere. The magnon mode is coupled to the MW cavity mode via a linear beam splitter interaction. As reported by Benrass et al. (Int. J. Mod. Phys. B 36, 2250036, 2022), it has been shown that the logarithmic negativity remains nonzero in the coexistence zone, illustrating why the latter includes entangled states. Additionally, a novel method for quantifying entanglement in quantum systems based on purity was introduced. Based on this, the main objective of this work is to examine how purity can be taken as evidence for the mixedness and entanglement that characterize the cavity-cavity and the magnon-magnon subsystems. A comparison of the entanglement behaviors with those obtained for purity under the influence of different parameters demonstrates that this resembles the use of purity as a feature and a quantification of the degree of entanglement in the two-mode symmetric state.