Quantumness near the Schwarzschild black hole based on W-state

TL;DR

The paper studies how Hawking radiation from a Schwarzschild black hole affects quantum resources for a W state, using $C_{l1}$, FOС $D$, CF $F$, and GC $Q$ across scenarios with three, two, or one accessible modes. By quantizing the Dirac field and applying Bogoliubov transformations, it reveals that Hawking radiation can simultaneously degrade coherence and enhance entanglement in the fully accessible case, while in reduced-access scenarios the Hawking temperature $T$ generally boosts both coherence and entanglement, stabilizing at nonzero values. When amplitude-damping noise is added, the results show a consistent pattern of coherence degradation but persistent or strengthened entanglement in the fully accessible case, with the other scenarios following noiseless trends. Overall, the study demonstrates a rich relational structure between relativity-induced effects and multipartite quantum resources, suggesting further investigations into other forms of quantumness in curved spacetime.

Abstract

We investigate certain quantumness in the vicinity of the Schwarzschild black hole by utilizing the W state. We explore the influence of the Hawking effect on the l_1-norm of quantum coherence, the first-order coherence (FOC), the concurrence-fill (CF) and the global concurrence (GC) in Schwarzschild black hole, for systems with one, two and three physically accessible modes. We conclude that the Hawking effect of the black hole not only disrupts but also enhance the quantum entanglement, while destroying the quantum coherence for systems with three physically accessible modes. For systems with one or two physically accessible modes, the Hawking effect exerts a positive influence on quantum coherence and quantum entanglement. Moreover, we study the influence of both the Hawking effect and environmental noise (AD channels) on l_1-norm of quantum coherence, FOC, CF and GC. It is demonstrated that for systems with three physically accessible modes, the Hawking effect of the black hole disrupts quantum coherence but exerts a positive influence on quantum entanglement under the AD channels.

Figures (6)

• Figure 1: The $l_{1}$-norm of quantum coherence $[C_{l_{1}}(\rho_{ABC})]$, FOC $[D(\rho_{ABC})]$, GC $[Q(\rho_{ABC})]$, CF $[F(\rho_{ABC})]$, and $D^{2}(\rho_{ABC})+F(\rho_{ABC})$ as functions of the Hawking temperature $T$ with $\omega=1$.
• Figure 2: The $l_{1}$-norm of quantum coherence $[C_{l_{1}}(\rho_{Abc})]$, FOC $[D(\rho_{Abc})]$, GC $[Q(\rho_{Abc})]$, CF $[F(\rho_{Abc})]$, and $D^{2}(\rho_{Abc})+F(\rho_{Abc})$ as functions of the Hawking temperature $T$ with $\omega=1$.
• Figure 3: The $l_{1}$-norm of quantum coherence $[C_{l_{1}}(\rho_{ABc})]$, FOC $[D(\rho_{ABc})]$, GC $[Q(\rho_{ABc})]$, CF $[F(\rho_{ABc})]$, and $D^{2}(\rho_{ABc})+F(\rho_{ABc})$ as functions of the Hawking temperature $T$ with $\omega=1$.
• Figure 4: The $l_{1}$-norm of quantum coherence $[C_{l_{1}}(\rho'_{ABC})]$, FOC $[D(\rho'_{ABC})]$, GC $[Q(\rho'_{ABC})]$, CF $[F(\rho'_{ABC})]$, and $D^{2}(\rho'_{ABC})+F(\rho'_{ABC})$ as functions of the Hawking temperature $T$ with $\omega=1$ for different $\gamma$: $\gamma=1/3$, $\gamma=1/2$ and $\gamma=2/3$.
• Figure 5: The $l_{1}$-norm of quantum coherence $[C_{l_{1}}(\rho'_{Abc})]$, FOC $[D(\rho'_{Abc})]$, GC $[Q(\rho'_{Abc})]$, CF $[F(\rho'_{Abc})]$, and $D^{2}(\rho'_{Abc})+F(\rho'_{Abc})$ as functions of the Hawking temperature $T$ with $\omega=1$ for different $\gamma$: $\gamma=1/3$, $\gamma=1/2$ and $\gamma=2/3$.