Distinguishing Black Hole Microstates using Holevo Information

Abstract

We use the Holevo information in a two-dimensional conformal field theory (CFT) with a large central charge $c$ to distinguish microstates from the underlying thermal state. Holographically, the CFT microstates of a thermal state are dual to black hole microstate geometries in three-dimensional anti-de Sitter space. It was found recently that the holographic Holevo information shows plateau behaviors at both short and long interval regions. This indicates that the black hole microstates are indistinguishable from the thermal state by measuring over a small region, and perfectly distinguishable over a region with its size comparable to the whole system. In this letter, we demonstrate that the plateaus are lifted by including the $1/c$ corrections from both the vacuum and non-vacuum conformal families of CFT in either the canonical ensemble or microcanonical ensemble thermal state. Our results imply that the aforementioned indistinguishability and distinguishability of black hole microstate geometries from the underlying black hole are spoiled by higher order Newton constant $G_N$ corrections of quantum gravity.

arXiv commentV1, 5+7 pages, 3 figures; V2, discussions on numbers of primary and descendant states refined; V3, 5+7 page, 1+2 figures, references added, published version

References in corpus (31)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The Black Hole in Three Dimensional Space Time
• Entanglement Entropy and Quantum Field Theory
• A Covariant Holographic Entanglement Entropy Proposal
• Quantum corrections to holographic entanglement entropy
• Entanglement Renyi entropies in holographic theories
• Logarithmic Corrections to Black Hole Entropy from the Cardy Formula
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Holographic entanglement beyond classical gravity
• Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
• Subsystem ETH
• A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots
• On short interval expansion of Rényi entropy
• Holographic Rényi entropy for CFT with $W$ symmetry
• ETH and Modular Invariance of 2D CFTs
• Entanglement entropy of two disjoint intervals from fusion algebra of twist fields
• A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled
• Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT
• Entanglement Entropy of Non-Unitary Integrable Quantum Field Theory
• On Distinguishability of Black Hole Microstates
• Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis
• Thermality and excited state Rényi entropy in two-dimensional CFT
• Short interval expansion of Rényi entropy on torus
• Holographic Calculation for Large Interval Rényi Entropy at High Temperature
• On the next-to-leading holographic entanglement entropy in $Ad{S}_3/CF{T}_2$
• Universal relation between thermal entropy and entanglement entropy in CFT
• On one-loop entanglement entropy of two short intervals from OPE of twist operators
• Corrections to holographic entanglement plateau
• Corrections in the relative entropy of black hole microstates

Cited by in corpus (12)

• Quantum Information Scrambling in Quantum Many-body Scarred Systems
• Distinguishing Random and Black Hole Microstates
• Note on ETH of descendant states in 2D CFT
• Entanglement spectrum of geometric states
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
• Black Remnants from T-Duality
• Rényi entropy at large energy density in 2D CFT
• Probing Black Hole Microstate Evolution with Networks and Random Walks
• Revealing quantum operator scrambling via measuring Holevo information on digital quantum simulators
• Perturbative distinguishability of black hole microstates from AdS/CFT correspondence
• Subsystem fidelity in two-dimensional conformal field theories
• Correlations in geometric states