The holographic dual of Rényi relative entropy
arXiv:1904.08433 · doi:10.1007/JHEP08(2019)099
Abstract
The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT) reduced to a spherical region. For example, when the excited state is a small perturbation of the vacuum state, the relative entropy is known to have a universal expression for \textit{all} CFT's \cite{Faulk-GR-entanglement}. Specifically, the perturbative relative entropy can be written as the symplectic flux of a certain scalar field in an \textit{auxiliary} AdS-Rindler spacetime \cite{Faulk-GR-entanglement}. Moreover, if the CFT has a semi-classical holographic dual, the relative entropy is known to be related to conserved charges in the bulk dual spacetime \cite{lashkari2016gravitational}. In this paper, we introduce a one-parameter generalization of the relative entropy which we call \textit{refined} Rényi relative entropy. We study this quantity in CFT's and find a one-parameter generalization of the aforementioned known results about the relative entropy. We also discuss a new family of positive energy theorems in asymptotically locally AdS spacetimes that arises from the holographic dual of the refined Rényi relative entropy.
arXiv comment37 pages, 3 figures. V3: added references
References in corpus (59)
- Gauge Theory Correlators from Non-Critical String Theory
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Black Hole Entropy is Noether Charge
- Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
- A Covariant Holographic Entanglement Entropy Proposal
- Towards a derivation of holographic entanglement entropy
- Generalized gravitational entropy
- On quantum Renyi entropies: a new generalization and some properties
- A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
- Notes on Some Entanglement Properties of Quantum Field Theory
- Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
- Relative entropy equals bulk relative entropy
- Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
- Gravitation from Entanglement in Holographic CFTs
- Gravitational Dynamics From Entanglement "Thermodynamics"
- Relative Entropy and Holography
- The Gravity Dual of Renyi Entropy
- A Quantum Focussing Conjecture
- Relative entropy and the Bekenstein bound
- Deriving covariant holographic entanglement
- Sandwiched Rényi Divergence Satisfies Data Processing Inequality
- A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
- Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
- Monotonicity of a relative Rényi entropy
- Bulk locality from modular flow
- The Holographic Entropy Cone
- Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
- Stability of Black Holes and Black Branes
- Modular Hamiltonians on the null plane and the Markov property of the vacuum state
- Nonlinear Gravity from Entanglement in Conformal Field Theories
- Holographic Renyi Entropy from Quantum Error Correction
- Entanglement Wedge Reconstruction via Universal Recovery Channels
- Entropy on a null surface for interacting quantum field theories and the Bousso bound
- Relative Entropies in Conformal Field Theory
- Bulk Emergence and the RG Flow of Entanglement Entropy
- Canonical Energy is Quantum Fisher Information
- Entanglement entropy across a deformed sphere
- Entanglement Entropy: A Perturbative Calculation
- Tomography from Entanglement
- Universality in the geometric dependence of Renyi entropy
- From Euclidean Sources to Lorentzian Spacetimes in Holographic Conformal Field Theories
- Entanglement Entropy for Relevant and Geometric Perturbations
- Relative entropy and the RG flow
- A proof of the generalized second law for rapidly-evolving Rindler horizons
- Gravitational Positive Energy Theorems from Information Inequalities
- Constraining gravity using entanglement in AdS/CFT
- Constraining Quantum Fields using Modular Theory
- Energy is Entanglement
- On Distinguishability of Black Hole Microstates
- Entanglement entropy, planar surfaces, and spectral functions
- Local Modular Hamiltonians from the Quantum Null Energy Condition
- Comment on the Bekenstein bound
- The Positivity of Energy for Asymptotically Anti-de Sitter Spacetimes
- Renyi relative entropies and renormalization group flows
- Holographic second laws of black hole thermodynamics
- The holographic entropy zoo
- On the Shape Dependence of Entanglement Entropy
- Dynamics of the Area Law of Entanglement Entropy
- Nonlinear constraints on gravity from entanglement
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- Quantum hypothesis testing in many-body systems
- Proof of Renyi QNEC for free fermions
- Holographic Rényi relative divergence in JT gravity
- Generalized Off-Shell ADT Conserved Charges in the Presence of Matter Chern-Simons Term