Resilience of Quantum Teleportation Fidelity for Bipartite Mixed States near Schwarzschild and Dilaton Black Holes

TL;DR

This work analyzes quantum teleportation fidelity for bipartite channels derived from tripartite GHZ and W states in curved spacetime near Schwarzschild and GHS Dilaton black holes. By quantizing Dirac fields, constructing Kruskal modes, and applying Bogoliubov transformations, the authors model Hawking-radiation-induced degradation and obtain the resulting bipartite states after tracing inaccessible modes. They show that GHZ-derived channels lose bipartite entanglement and fail as teleportation channels, while W-derived channels retain sufficient bipartite entanglement to achieve fidelities above the classical bound $f>\frac{2}{3}$; in Schwarzschild spacetime, fidelities lie roughly in $[0.715,0.745]$, and in Dilaton spacetime in $[0.709,0.712]$ across parameter ranges. The results highlight the resilience of teleportation under relativistic gravitational effects and motivate further exploration of quantum information processing in curved spacetime across additional states and black-hole models.

Abstract

We investigate the robustness of quantum teleportation in the presence of strong gravitational fields by analysing bipartite mixed states derived from tripartite GHZ and W-class states near black hole event horizons. Considering a scenario where two observers approach the horizon of either a Schwarzschild or a Garfinkle Horowitz Strominger (GHS) Dilaton black hole while a third remains in flat space, we quantify the teleportation fidelity of the resulting bipartite channels after tracing out one party. Through the quantization of Dirac fields and Bogoliubov transformations, we compute the teleportation fidelity under the influence of Hawking radiation and spacetime curvature. Our results show that while entanglement degrades, teleportation fidelity remains above the classical threshold of $f>\frac{2}{3}$ for channels derived from W-class states, but not for GHZ-derived states. This indicates that quantum teleportation can remain feasible near black holes provided the initial entangled state retains useful bipartite entanglement.

Figures (10)

• Figure 1: The schematic diagram shows that the $3$ qubit states being exposed near the event horizon of the black hole.
• Figure 2: We plot the tangle of the $GHZ$ state against monochromatic frequency ($\omega$) and Hawking temperature ($T$). Fig.(A) shows the variation of tangle $\tau(\rho_{GHZ}^{wfabc})$ when Hawking temperature ($T$) is varied from $0$ to $5$ and monochromatic frequency ($\omega$) is varied from $0$ to $10000$ in the background of Schwarzschild black hole. Fig.(B) shows the variation of same $\tau(\rho_{GHZ}^{wfabc})$ when charge ($Q$) is varied from $0$ to $20$ and monochromatic frequency ($\omega$) is varied from $0$ to $50$ in the backdrop of Dilaton black hole.
• Figure 3: Variation of concurrence of bipartite mixed states $\rho_{W}^{wfac}$ (or $\rho_{W}^{wfab}$) derived from tripartite prototype $W$ states in the background of Schwarzschild black hole. Fig.(a) is the $3D$ depiction of the variation of $C(\rho_{W}^{wfac})$ against monochromatic frequency ($\omega$) and Hawking temperature ($T$), while $\omega$ is varied from $0$ to $1$, $T$ is varied from $1$ to $10$. Fig.(b) is the $2D$ plot of concurrence against $T$ and fig.(c) is the $2D$ plot concurrence against $\omega$.
• Figure 4: Variation of concurrence of bipartite mixed states $\rho_{W}^{wfac}$ (or $\rho_{W}^{wfab}$) derived from tripartite prototype $W$ states in the background of Dilaton black hole. Fig.(a) is the $3D$ depiction of the variation of $C(\rho_{W}^{wfac})$ against monochromatic frequency ($\omega$) and Dilaton parameter ($D$), while $\omega$ is varied from $0$ to $1$, $D$ is varied from $1$ to $10$. Fig.(b) is the $2D$ plot of concurrence against $D$ and fig.(c) is the $2D$ plot concurrence against $\omega$.
• Figure 5: Variation of teleportation fidelity of bipartite mixed states $\rho_{W}^{wfac}$ (or $\rho_{W}^{wfab}$) derived from tripartite prototype $W$ states in the background of Schwarzschild black hole. $T$ is varied from $1$ to $10$ and $\omega$ is varied from $0$ to $1$. Fig.(b) shows variation of teleportation fidelity against $T$ and fig. (c) shows variation of teleportation fidelity against $\omega$.