Quantum tasks require islands on the brane

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.

arXiv commentv4: typo fixes

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• Holographic BCFTs and Communicating Black Holes
• Entanglement Phase Structure of a Holographic BCFT in a Black Hole Background
• Defect Extremal Surface for Reflected Entropy
• Causal Structures and Nonlocality in Double Holography
• BCFT in a Black Hole Background: An Analytical Holographic Model
• Page Curve of Effective Hawking Radiation
• Bounds on gravitational brane couplings and tomography in AdS3 black hole microstates
• The connected wedge theorem and its consequences
• Holographic complexity: braneworld gravity versus the Lloyd bound
• Bulk private curves require large conditional mutual information
• Exploring causality in braneworld/cutoff holography via holographic scattering
• Page Curve of AdS-Vaidya Model for Evaporating Black Holes
• Page Curve from Defect Extremal Surface and Island in Higher Dimensions
• Cryptographic tests of the python's lunch conjecture
• Conformal Rigidity from Focusing