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

Abstract

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.

Figures (4)

• Figure 1: Multipartite mutual information $I^{\mathrm{GHZ}}_{B}(N)$ of bosonic GHZ state as a function of the dilaton $\mathcal{D}$ for systems with $N=5$ (a) and $N=10$ (b), shown at different field mode frequencies $\omega$.
• Figure 2: Mutual information $I^{\mathrm{W}}_{B}(N)$ for W state of bosonic field as a function of the dilaton $\mathcal{D}$ for systems with $N=5$ (a) and $N=10$ (b), shown at different field mode frequencies $\omega$.
• Figure 3: Multipartite mutual information $I^{\mathrm{GHZ}}_{F}(N)$ of fermionic GHZ state as a function of the dilaton $\mathcal{D}$, shown for systems with $N=5$ and $N=10$ particles at different field mode frequencies $\omega$.
• Figure 4: Mutual information $I^{\mathrm{W}}_{F}(N)$ for fermionic W state and REC for bosonic and fermionic GHZ and W states as a function of the dilaton parameter $\mathcal{D}$ for a fixed $N=5$ at different mode frequencies $\omega$.