Does fermionic entanglement always outperform bosonic entanglement in dilaton black hole?

TL;DR

This work challenges the prevailing belief that fermionic entanglement universally outperforms bosonic entanglement in relativistic settings by analyzing genuine $N$-partite entanglement of bosonic and fermionic GHZ states in a Garfinkle-Horowitz-Strominger dilaton black hole. Using negativity-based measures (one-tangle, two-tangle, and $ ext{π}_{4}$-tangle), it reveals partition- and gravity-strength dependent outcomes: bosonic entanglement can exceed fermionic entanglement in non-gravitational vs. gravitational mode partitions, while fermionic entanglement can dominate the gravitational vs. rest partition; moreover, a nonmonotonic crossover in global multipartite entanglement occurs as the dilaton $oldsymbol{ extepsilon}$ grows. The results depend on the number of near-horizon modes $oldsymbol{m}$ and extend to general $oldsymbol{N}$, highlighting a nuanced, partition-sensitive interplay between field statistics and curved spacetime. These findings have implications for selecting quantum resources in relativistic quantum information tasks under extreme gravitational conditions.

Abstract

It has traditionally been believed that fermionic entanglement generally outperforms bosonic entanglement in relativistic frameworks, and that bosonic entanglement experiences sudden death in extreme gravitational environments. In this study, we analyze the genuine N-partite entanglement, measured by negativity, of bosonic and fermionic GHZ states, focusing on scenarios where a subset of $m$ ($m<N$) constituents interacts with Hawking radiation generated by a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. Surprisingly, we find that quantum entanglement between the non-gravitational and gravitational modes for the bosonic field is stronger than that in the same modes for the fermionic field within dilaton spacetime. This study challenges the traditional belief that ``fermionic entanglement always outperforms bosonic entanglement" in the relativistic framework. However, quantum entanglement between the gravitational modes and the combined gravitational and non-gravitational modes is weaker for the bosonic field than for the fermionic field in the presence of a dilaton black hole. Finally, the connection between the global N-partite entanglement in the bosonic field and that in the fermionic field is influenced by the gravitational field's intensity. Our study reveals the intrinsic relationship between quantum entanglement of bosonic and fermionic fields in curved spacetime from a new perspective, and provides theoretical guidance for selecting appropriate field-based quantum resources for relativistic quantum information tasks under extreme gravitational conditions.

Figures (5)

• Figure 1: Schematic diagram of our physical model with $N-m$ particles in a flat region, and $m$ particles near the event horizon of a dilaton black hole.
• Figure 2: The one-tangle of the GHZ state for bosonic and fermionic fields as a function of the dilaton $\epsilon$ for the fixed values $M=\omega=1$.
• Figure 3: Tetrapartite $\pi$-tangle of bosonic and fermionic fields versus the dilaton $\epsilon$, with fixed $M=\omega=1$.
• Figure 4: N‑partite one‑tangle of the GHZ states between the non‑gravitational and gravitational modes for bosonic and fermionic fields as a function of the dilaton $\epsilon$, with $M=\omega=1$.
• Figure 5: N‑partite one‑tangle of the GHZ states between the gravitational modes and the combined gravitational and non-gravitational modes for bosonic and fermionic fields as a function of the dilaton $\epsilon$, with $M=\omega=1$.