Tripartite Entanglement of Hawking Radiation in Dispersive Model

TL;DR

This paper analyzes the multipartite entanglement structure of Hawking radiation in a dispersive model, revealing persistent tripartite entanglement across frequencies and deviations from the partner mode picture at high frequencies.

Contribution

It provides an exact form of the tripartite in-vacuum state and demonstrates the persistence of genuine tripartite entanglement in a dispersive Hawking radiation model.

Findings

Genuine tripartite entanglement persists across all frequencies up to the cutoff.

In low frequencies, tripartite entanglement is small compared to bipartite entanglement.

Near the cutoff, entanglement is shared among three modes, challenging the partner mode picture.

Abstract

We investigate entanglement of the Hawking radiation in a dispersive model with subluminal dispersion. In this model, feature of the Hawking radiation is represented by three mode Bogoliubov transformation connecting the in-vacuum state and the out-state. We obtain the exact form of the tripartite in-vacuum state which encodes structure of multipartite entanglement. Bogoliubov coefficients are computed by numerical calculation of the wave equation with subluminal dispersion and it is found that genuine tripartite entanglement persists in whole frequency range up to the cutoff arisen from the subluminal dispersion. In the low frequency region, amount of genuine tripartite entanglement is small compared to bipartite entanglement between the Hawking particle and its partner mode, and the deviation from the thermal spectrum is negligible. On the other hand, in the high frequency region near the cutoff, entanglement is equally shared by two pairs of three modes and the partner picture of the Hawking radiation does not hold.