Entanglement metrics for $B$ Meson system

The $B$-factory experiments operate at electron-positron colliders with beam energies precisely tuned for optimal $B^{0}\text{-}\bar{B}^{0}$ meson pair production. These $B^{0}\text{-}\bar{B}^{0}$ meson pairs are produced entangled and offer a unique opportunity to explore quantum correlations and examine the foundational aspects of quantum mechanics. In this work, we present a comprehensive analysis of entanglement metrics in the $B$-meson system within the framework of open quantum systems, which introduces decoherence due to interactions with the environment. We examine several distinct entanglement measures, each highlighting different facets of quantum entanglement and its sensitivity to decoherence effects. We further analyze the impact of decoherence by systematically varying the decoherence parameter across different scales.