Quantum Tasks in Holography

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 talk 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 in simple models Islands on the brane are causally connected to their corresponding radiation systems.