Relation between time-dependent entropy and the partner-mode vacuum state

Clarify the relation between the time-dependent entanglement entropy associated with the Page curve and the time-independent vacuum state that explicitly contains the Rindler partner modes and Milne Hawking modes.

Background

The paper constructs a time-independent entangled vacuum state in terms of Rindler and Milne modes and shows that local squeezing changes measured correlations without changing the entanglement entropy of the mode pair.

It also refers to the time-dependent entanglement entropy of the moving-mirror model, which follows a Page-curve-like behavior when the partner mode becomes accessible. The precise relationship between these two descriptions is left unresolved.

References

Another open question is whether we can compute the entropy (or second Renyi entropy) of part of the Hawking radiation, and determine whether part of the infalling modes at the future horizon are in its entanglement island.

— Blast freezing a black hole  (2609.28962 - Akhtar et al., 24 Sep 2026) in Section “Interior dynamics and future directions”

However, the relation between the time-dependent entanglement entropy and the time-independent vacuum state that explicitly involves the notion of partner modes developed in this paper is not clear.

— Squeezed quantum states and partner modes in the moving mirror model of black hole evaporation  (2608.11957 - Lin et al., 12 Aug 2026) in Section “Discussions and summary,” subsection “Entanglement entropy vs. quantum correlation”