Multiqubit coherence of mixed states near event horizon

Abstract

We investigate the coherence of mixed Greenberger-Horne-Zeilinger (GHZ) and W states for bosonic and fermionic fields when a subset of $n$ ($n<N$) qubits experiences Hawking radiation near a Schwarzschild black hole. Analytical expressions are derived for the coherence of mixed N-qubit systems, including both the physically accessible and inaccessible parts in curved spacetime. The results show that the mixed W state maintains its coherence more effectively than the GHZ state as the Hawking temperature increases, even though its entanglement is weaker. As the number of qubits grows, W-state coherence becomes increasingly resistant to gravitational decoherence. Furthermore, fermionic fields preserve stronger entanglement, while bosonic fields retain higher coherence, highlighting a clear contrast between different particle statistics. These findings demonstrate how the Schwarzschild spacetime reshapes the balance between quantum coherence and entanglement, offering guidance for future relativistic quantum information applications.

Figures (9)

• Figure 1: Schematic diagram of our physical model with $N-n$ observers in a flat region, and $n$ observers near the event horizon of a Schwarzschild black hole.
• Figure 2: Schematic diagram illustrating the numbers of physically accessible and inaccessible modes in the Schwarzschild black hole.
• Figure 3: The physically accessible coherence $C^{B}(GHZ)$ and $C^{B}(W)$ of bosonic field as functions of the Hawking temperature $T$ for different $p$ and $x$, where we have fixed $M=\omega=1$.
• Figure 4: The physically inaccessible coherence $C^{B}(GHZ)$ and $C^{B}(W)$ of bosonic field as functions of the Hawking temperature $T$ for different $N$, $p$, $x$, and $n$, with fixed parameters $M=\omega=1$.
• Figure 5: Quantum coherence $C^{B}(GHZ)$ and $C^{B}(W)$ of bosonic field as functions of $x$ and $n$, where we have fixed $M=\omega=1$, and $T=20$. In Fig (a) and (c), the mixing parameter is set to $p=0.2$, while in Fig (b) and (d), it is fixed at $p=0.5$.