Bosonic and fermionic mutual information of N-partite systems in dilaton black hole background

We investigate multipartite quantum correlations by analyzing the mutual information of N-partite states for both free bosonic and fermionic fields in the background of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. Focusing on multipartite GHZ and W states, we examine how the Hawking effect influences the N-partite mutual information when one observer hovers near the event horizon while the remaining observers stay in the asymptotically flat region. By tracing over the inaccessible modes inside the event horizon, we derive analytical expressions for the N-partite mutual information in dilaton spacetime for both bosonic and fermionic fields. Our results show that fermionic mutual information is larger than its bosonic counterpart under the influence of the dilaton black hole, whereas the fermionic relative entropy of coherence (REC) is smaller than the bosonic REC. Moreover, the mutual information of GHZ states is consistently larger than that of W states, while the REC of GHZ states is smaller than that of W states in curved spacetime. These findings indicate that the choice of quantum resources should be tailored to the particle species and state structure in relativistic quantum information tasks to optimize their operational efficiency.

💡 Research Summary

The paper investigates multipartite quantum correlations in the background of a Garfinkle‑Horowitz‑Strominger (GHS) dilaton black hole, focusing on the quantum mutual information (QMI) of N‑partite Greenberger‑Horne‑Zeilinger (GHZ) and W states for both free bosonic (scalar) and fermionic (spin‑½) fields. The authors first quantize the scalar and Dirac fields on the GHS metric, which is characterized by the mass M and dilaton parameter D (related to the magnetic charge). By solving the field equations near the event horizon and introducing Kruskal coordinates, they derive Bogoliubov transformations that relate the creation‑annihilation operators in the Kruskal frame to those in the static dilaton frame. For bosons the transformation yields a thermal Bose‑Einstein spectrum N_B(ω)=1/(e^{8π ω (M−D)}−1); for fermions it yields a Fermi‑Dirac spectrum N_F(ω)=1/(e^{8π ω (M−D)}+1).

The authors then consider an N‑party scenario (N≥3) in which all observers initially share either a GHZ or a W state in the asymptotically flat region. One observer (the N‑th) moves to hover just outside the black‑hole horizon, while the remaining N‑1 observers stay far away. Because the interior modes are causally inaccessible, the authors trace over them, obtaining reduced density matrices for the exterior region. For the bosonic case the Kruskal vacuum is expressed as an infinite‑dimensional two‑mode squeezed state; the GHZ and W states are rewritten in terms of exterior and interior mode operators. After tracing out the interior, the resulting density matrix has a block‑diagonal structure with 2×2 blocks, each of which can be diagonalized analytically. An analogous procedure is carried out for fermions, with the key difference that the Bogoliubov coefficients involve the Fermi‑Dirac factor.

Multipartite mutual information is defined as I_N = Σ_i S(ρ_i) – S(ρ_{1…N}), where S denotes the von Neumann entropy. Using the reduced exterior density matrices, the authors compute I_N for both statistics and both state families. Their analytical results show that as the dilaton parameter D increases (i.e., as the black hole approaches the extremal limit M→D), the QMI monotonically decreases and approaches a constant value independent of the field frequency ω. Crucially, for any given D and ω, the fermionic QMI remains larger than the bosonic QMI, indicating that fermionic correlations are more robust against Hawking‑induced degradation.

State‑structure effects are also highlighted. GHZ states, which possess maximal global entanglement, consistently yield higher QMI than W states, reflecting the stronger total correlations present in GHZ. Conversely, the relative entropy of coherence (REC) behaves oppositely: W states have larger REC than GHZ states, because GHZ concentrates coherence in a single global superposition while W distributes coherence more evenly among its components.

The paper concludes that both particle statistics and the specific multipartite entanglement pattern critically determine the resilience of quantum correlations in curved spacetime. These findings have practical implications for relativistic quantum information tasks such as long‑distance quantum communication, distributed quantum computation, and quantum networking in gravitational environments. Selecting fermionic resources when robustness is paramount, or choosing GHZ versus W states depending on whether total correlations or coherence distribution is more valuable, can optimize operational efficiency under the influence of a dilaton black hole.