Distinguishing Random and Black Hole Microstates
arXiv:2108.00011 · doi:10.1103/PRXQuantum.2.040340
Abstract
This is an expanded version of the short report [Phys. Rev. Lett. 126, 171603 (2021)], where the relative entropy was used to distinguish random states drawn from the Wishart ensemble as well as black hole microstates. In this work, we expand these ideas by computing many generalizations including the Petz Rényi relative entropy, sandwiched Rényi relative entropy, fidelities, and trace distances. These generalized quantities are able to teach us about new structures in the space of random states and black hole microstates where the von Neumann and relative entropies were insufficient. We further generalize to generic random tensor networks where new phenomena arise due to the locality in the networks. These phenomena sharpen the relationship between holographic states and random tensor networks. We discuss the implications of our results on the black hole information problem using replica wormholes, specifically the state dependence (hair) in Hawking radiation. Understanding the differences between Hawking radiation of distinct evaporating black holes is an important piece of the information problem that was not addressed by entropy calculations using the island formula. We interpret our results in the language of quantum hypothesis testing and the subsystem eigenstate thermalization hypothesis (ETH), deriving that chaotic (including holographic) systems obey subsystem ETH for all subsystems less than half the total system size.
arXiv comment57 pages
References in corpus (86)
- Quantum Computing in the NISQ era and beyond
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Entanglement Entropy and Quantum Field Theory
- Chaos and Quantum Thermalization
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Aspects of Holographic Entanglement Entropy
- Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long Distances
- Geometric and Renormalized Entropy in Conformal Field Theory
- Average Entropy of a Subsystem
- Black holes as mirrors: quantum information in random subsystems
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Generalized gravitational entropy
- Information in Black Hole Radiation
- Replica Wormholes and the Entropy of Hawking Radiation
- Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
- Quantum corrections to holographic entanglement entropy
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
- Bulk Locality and Quantum Error Correction in AdS/CFT
- Time Evolution of Entanglement Entropy from Black Hole Interiors
- The entropy of Hawking radiation
- On quantum Renyi entropies: a new generalization and some properties
- Operator Spreading in Random Unitary Circuits
- Eigenstate Thermalization Hypothesis
- Notes on Some Entanglement Properties of Quantum Field Theory
- The Quantum Chernoff Bound
- Relative entropy equals bulk relative entropy
- Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
- Holographic duality from random tensor networks
- Induced measures in the space of mixed quantum states
- The Ryu-Takayanagi Formula from Quantum Error Correction
- The Gravity Dual of Renyi Entropy
- Does a single eigenstate encode the full Hamiltonian?
- Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
- Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
- Generating random density matrices
- Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
- Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
- Subsystem ETH
- Flat entanglement spectra in fixed-area states of quantum gravity
- Holographic entanglement plateaux
- Statistical properties of random density matrices
- Average fidelity between random quantum states
- Holographic Renyi Entropy from Quantum Error Correction
- alpha-z-relative Renyi entropies
- Black Hole Microstate Cosmology
- Optimal sequence of quantum measurements in the sense of Stein's lemma in quantum hypothesis testing
- Random matrix techniques in quantum information theory
- Product of Ginibre matrices: Fuss-Catalan and Raney distributions
- Renyi Entropy of Chaotic Eigenstates
- Thermodynamic entropy of a many body energy eigenstate
- Entanglement measures and their properties in quantum field theory
- Modular Hamiltonian of Excited States in Conformal Field Theory
- Structure of chaotic eigenstates and their entanglement entropy
- Principles of Quantum Communication Theory: A Modern Approach
- The Converse Part of The Theorem for Quantum Hoeffding Bound
- Pure states in the SYK model and nearly- gravity
- A quantum version of Sanov's theorem
- Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories
- Unitary designs from statistical mechanics in random quantum circuits
- Asymptotics of random density matrices
- Discriminating quantum states: the multiple Chernoff distance
- Subsystem Trace Distance in Quantum Field Theory
- Relative entropy of excited states in conformal field theories of arbitrary dimensions
- Distinguishability of generic quantum states
- Probing phase transitions of holographic entanglement entropy with fixed area states
- Random graph states, maximal flow and Fuss-Catalan distributions
- Enhanced corrections near holographic entanglement transitions: a chaotic case study
- On Distinguishability of Black Hole Microstates
- Gaussianization and eigenvalue statistics for random quantum channels (III)
- Relative Entropy of Random States and Black Holes
- Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination
- Entanglement of Local Operators and the Butterfly Effect
- Coarse-grained dynamics of operator and state entanglement
- Universal relation between Green's functions in random matrix theory
- Wishart and random density matrices: Analytical results for the mean-square Hilbert-Schmidt distance
- Spectral density of generalized Wishart matrices and free multiplicative convolution
- Distinguishing Black Hole Microstates using Holevo Information
- Eigenstate Thermalization Hypothesis in Conformal Field Theory
- Corrections in the relative entropy of black hole microstates
- Random density matrices: Analytical results for mean root fidelity and mean square Bures distance
- Exponential error rates in multiple state discrimination on a quantum spin chain
- Spectral statistics for the difference of two Wishart matrices
- Void formation in operator growth, entanglement, and unitarity
- The Markov gap for geometric reflected entropy
- Interpolating between symmetric and asymmetric hypothesis testing
Cited by in corpus (14)
- Negativity Spectra in Random Tensor Networks and Holography
- Rényi Mutual Information in Quantum Field Theory
- Defect extremal surfaces for entanglement negativity
- Quantum thermodynamics of holographic quenches and bounds on the growth of entanglement from the QNEC
- Microstructure in matrix elements
- Beyond islands: A free probabilistic approach
- Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
- Subsystem distances between quasiparticle excited states
- A comment on a fine-grained description of evaporating black holes with baby universes
- Trace distance between fermionic Gaussian states from a truncation method
- Large and Small Corrections to the JLMS Formula from Replica Wormholes
- The Holographic Map of an Evaporating Black Hole
- Subsystem Trace-Distances of Two Random States
- On Quantum Information Before the Page Time