One-shot holography

Abstract

Following the work of [2008.03319], we define a generally covariant max-entanglement wedge of a boundary region $B$, which we conjecture to be the bulk region reconstructible from $B$. We similarly define a covariant min-entanglement wedge, which we conjecture to be the bulk region that can influence the state on $B$. We prove that the min- and max-entanglement wedges obey various properties necessary for this conjecture, such as nesting, inclusion of the causal wedge, and a reduction to the usual quantum extremal surface prescription in the appropriate special cases. These proofs rely on one-shot versions of the (restricted) quantum focusing conjecture (QFC) that we conjecture to hold. We argue that these QFCs imply a one-shot generalized second law (GSL) and quantum Bousso bound. Moreover, in a particular semiclassical limit we prove this one-shot GSL directly using algebraic techniques. Finally, in order to derive our results, we extend both the frameworks of one-shot quantum Shannon theory and state-specific reconstruction to finite-dimensional von Neumann algebras, allowing nontrivial centers.

84 pages, 8 figures, v2 added clarifications

References in corpus (58)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Covariant Holographic Entanglement Entropy Proposal
• Generalized gravitational entropy
• A Covariant Entropy Conjecture
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Quantum corrections to holographic entanglement entropy
• Entanglement Renormalization and Holography
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Bulk Locality and Quantum Error Correction in AdS/CFT
• On quantum Renyi entropies: a new generalization and some properties
• The operational meaning of min- and max-entropy
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Relative entropy equals bulk relative entropy
• Holographic representation of local bulk operators
• Holographic duality from random tensor networks
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• Causality & holographic entanglement entropy
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Holographic Entanglement Entropy for General Higher Derivative Gravity
• A Quantum Focussing Conjecture
• Local bulk operators in AdS/CFT: a boundary view of horizons and locality
• Leftover Hashing Against Quantum Side Information
• An Algebra of Observables for de Sitter Space
• A Fully Quantum Asymptotic Equipartition Property
• Quantum state merging and negative information
• Theorems on gravitational time delay and related issues
• Gravity and the Crossed Product
• The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
• Large N algebras and generalized entropy
• One-shot decoupling
• Entanglement Wedge Reconstruction via Universal Recovery Channels
• A General Proof of the Quantum Null Energy Condition
• Chain Rules for Smooth Min- and Max-Entropies
• Generalized entropy for general subregions in quantum gravity
• The decoupling approach to quantum information theory
• Monotonicity of the Quantum Relative Entropy Under Positive Maps
• Learning the Alpha-bits of Black Holes
• Leading order corrections to the quantum extremal surface prescription
• Notes on the type classification of von Neumann algebras
• The Generalized Second Law implies a Quantum Singularity Theorem
• Quantum minimal surfaces from quantum error correction
• Single-shot Quantum State Merging
• Large Breakdowns of Entanglement Wedge Reconstruction
• Entanglement Wedges for Gravitating Regions
• Constraining Quantum Fields using Modular Theory
• The Smooth Entropy Formalism for von Neumann Algebras
• A Lower Bound on the Energy Density in Classical and Quantum Field Theories
• Covariant bit threads
• Quantum Complementarity through Entropic Certainty Principles
• Holographic Tensor Networks in Full AdS/CFT
• Random tensor networks with nontrivial links
• Approximate Quantum Error Correction Revisited: Introducing the Alpha-bit
• The black hole interior from non-isometric codes and complexity
• The holographic map as a conditional expectation
• Entanglement Wedge Reconstruction of Infinite-dimensional von Neumann Algebras using Tensor Networks
• Beyond islands: A free probabilistic approach
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Asymptotically isometric codes for holography

Cited by in corpus (8)

• Multipartite edge modes and tensor networks
• Minimal Areas from Entangled Matrices
• Relational bulk reconstruction from modular flow
• Extremality as a Consistency Condition on Subregion Duality
• Subregion duality, wedge classification and no global symmetries in AdS/CFT
• Hyperfine Structure of Quantum Entanglement
• Entangled universes
• Revisiting holographic codes with fractal-like boundary erasures