Entanglement metrics for $B$ Meson system

Abstract

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.

Figures (3)

• Figure 1: Relative Rényi entanglement entropy as a function of the decay time $t$ and the Rényi order $\alpha$ for different values of the decoherence parameter $\lambda$.
• Figure 2: Contour plots of entanglement measures for the $B^{0}\text{-}\bar{B}^{0}$ system as functions of decay time $t$ and decoherence parameter $\lambda$: (a) Relative entropy of entanglement $\varepsilon_R$, (b) Entanglement of formation $E_F$, (c) $\pi$-tangle $\tau_E$, and (d) Purity $\mathcal{P}$.The results illustrate the degradation of quantum correlations with increasing decoherence.
• Figure 3: The heat map represents Negativity $(N)$ and the contour line in white illustrates the constant logarithmic negativity $(E_N)$ for the entangled $B^{0}\text{-}\bar{B}^{0}$ meson system, displayed as a function of the decay time $t$ and the decoherence parameter $\lambda$.