Entanglement inequalities for timelike intervals within dynamical holography

TL;DR

This paper investigates entanglement inequalities for timelike intervals in dynamical holography, confirming some properties and revealing violations of strong subadditivity in specific setups.

Contribution

It extends previous work to two timelike subregions in AdS$_3$-Vaidya holography and analyzes entanglement inequalities, including violations of strong subadditivity.

Findings

Positivity of timelike mutual information confirmed.

Weak monotonicity holds for non-overlapping subregions.

Strong subadditivity is generally violated in overlapping intervals.

Abstract

This paper extends our previous work (arXiv:2504.14313) of a single timelike subregion to two, in the framework of AdS$_3$-Vaidya holography. We confirm the positivity of timelike mutual information and the statement of weak monotonicity when the subregions are non-overlapping. We also study entanglement inequalities such as Araki-Lieb inequality and strong subadditivity when the intervals start to overlap. In line with the recent findings in the literature, we provide explicit working examples showing that the timelike version of the strong subadditivity is generally violated in these setups, even though the statements of subadditivity and Araki-Lieb inequality hold true.