Survival of nonclassical correlations in Lorentz-violating spacetime

Abstract

The breakdown of Lorentz invariance, a potential signature of quantum gravity, offers a window into physics beyond general relativity. We investigate how such a violation, embodied by the Einstein-Bumblebee black hole spacetime, influences the nonlocal quantum correlations. Specifically, we study the quantum steering and Bell nonlocality between modes trapped inside and outside the event horizon of an Einstein-Bumblebee black hole. Our analysis demonstrates that quantum steering for an initially correlated state is confined to a narrow region near the event horizon, with the Lorentz-violating parameter further constraining this domain. Notably, the degree of steering asymmetry is significantly modulated by both the distance from the horizon and the Lorentz-violating parameter, with the two spatially separated regions exhibiting opposite trends. Furthermore, the Bell nonlocality measurable by an external observer strengthens with increasing distance from the black hole. These findings confirm the persistence of nonclassical correlations in a Lorentz-violating gravitational background and and offer a novel perspective on the interplay between quantum information and fundamental spacetime symmetries.

Figures (4)

• Figure 1: The steering $S^{R \rightarrow A}$ from Rob to Alice and the steering $S^{A \rightarrow R}$ from Alice to Rob vary with $R_{0}$ and $\ell$. The three segments of $R_{0}$ values from left to right increase from 2 to 3, where the color bar $\ell$ represents values ranging from 0.1 to 1, with $\omega=0.1$.
• Figure 2: (a) shows the variation of the steering $S^{\bar{R} \to A}$ from Anti-Rob to Alice and the steering $S^{A \to \bar{R}}$ from Alice to Anti-Rob with respect to $R_{0}$ and $\ell$. The values of $R_{0}$ in the two segments range from 2 to 3, with larger $R_{0}$ values on the left and smaller values on the right. (b) shows the variation of the steering from Anti-Rob to Rob $S^{\bar{R} \to R}$ and from Rob to Anti-Rob $S^{R \to \bar{R}}$ with respect to $R_{0}$ and $\ell$. The two segments of $R_{0}$ range from 2 to 3, with the upper segment having larger values and the lower segment having smaller values. Here, $\omega=0.1$, and the color bar $\ell$ represents values from 0.1 to 1.
• Figure 3: The values of $\Delta S_{AR}$, $\Delta S_{A\overline{R}}$, and $\Delta S_{R\overline{R}}$ as a function of $R_{0}$. Here, $\omega=0.1$ and $\ell=0.1$.
• Figure 4: The values of $B(\rho_{AR})$, $B(\rho_{A\overline{R}})$, and $B(\rho_{R\overline{R}})$ as a function of $R_{0}$. Here, $\omega=0.1$ and $\ell=0.1$.