Quantum tasks require islands on the brane

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 be 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.

Automated summary

The research argues that quantum computations with inputs and outputs distributed in spacetime impose constraints on entanglement in holographic theories, leading to the connected wedge theorem. By extending this work to AdS/BCFT context with an end-of-the-world brane, a new connected wedge theorem is discovered. This theorem is applied to brane models of black holes, showing the relationship between formation of islands in the Ryu-Takayanagi formula and causal features of the ambient spacetime.