Coherence of multipartite quantum states in the black hole quantum atmosphere

According to the recently introduced concept of quantum atmosphere, the black hole radiation is suggested to originate from the quantum excitations at the effective distance ($r$) near the event horizon ($r_H$). Here, this concept is explored from the quantum resource perspective by analysing the coherence of multipartite quantum systems located near a black hole. For the Greenberger-Horne-Zeilinger state, it is found that signatures of the atmosphere are apparent. This is to say, the coherence exhibits peak close to the event horizon and next decreases, recovering conventional behavior at $r/r_H \rightarrow\infty$. Interestingly, it is shown that as the quantum state gets more complex and the number of parties increases, the role of quantum atmosphere diminishes and the standard behaviour expected for the $N$-partite coherence quantifiers can be observed. That means, in case of complex setups the quantum atmosphere signatures may not be detectable. Hence, our findings show that care should be taken, regarding size of a system, when quantum atmosphere argument is considered.
Comment: 8 pages, 3 figures