Quantum tasks require islands on the brane

TL;DR

This paper extends the connected wedge theorem to AdS/BCFT with branes, linking island formation in black holes to causal structures, and demonstrates how information localization on the brane influences entanglement constraints.

Contribution

It introduces a new connected wedge theorem in AdS/BCFT with branes, relating island formation to causal connectivity and information localization on the brane.

Findings

Island formation occurs when the black hole interior is causally connected to radiation.

For constant tension branes in pure AdS, causal connection is both necessary and sufficient for island formation.

The theorem links entanglement constraints to causal structures in holographic models.

Abstract

In recent work, it was argued that quantum computations with inputs and outputs distributed in spacetime, or quantum tasks, impose constraints on entanglement in holographic theories. The resulting constraint was named the connected wedge theorem and can verified by a direct bulk proof using focusing arguments in general relativity. In this article we extend this work to the context of AdS/BCFT, where an end-of-the-world brane is present in the bulk. By considering quantum tasks which exploit information localized to the brane, we find a new connected wedge theorem. We apply this theorem to brane models of black holes, where it relates the formation of islands in the Ryu-Takayanagi formula to causal features of the ambient spacetime. In particular, we find that if the black hole interior is causally connected to the radiation system through the ambient spacetime, then an island forms. For constant tension branes in pure AdS the converse also holds.