Long-distance entanglement of purification and reflected entropy in conformal field theory
arXiv:2102.00013 · doi:10.1103/PhysRevLett.127.141604
Abstract
Quantifying entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy is a new and challenging subject. In this work, we study both quantities for two spherical subregions far away from each other in the vacuum of a conformal field theory in any number of dimensions. Using lattice techniques, we find an elementary proof that the decay of both, the entanglement of purification and reflected entropy, is enhanced with respect to the mutual information behaviour by a logarithm of the distance between the subregions. In the case of the Ising spin chain at criticality and the related free fermion conformal field theory, we compute also the overall coefficients numerically for the both quantities of interest.
arXiv comment5 pages, 2 figures + appendices; v2: previous results unchanged, added proof of the long-distance behaviour of EoP, reorganized presentation
References in corpus (50)
- Gauge Theory Correlators from Non-Critical String Theory
- The Large N Limit of Superconformal Field Theories and Supergravity
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Gaussian Quantum Information
- Entanglement Entropy and Quantum Field Theory
- A Covariant Holographic Entanglement Entropy Proposal
- Geometric and Renormalized Entropy in Conformal Field Theory
- Entanglement entropy and conformal field theory
- Generalized gravitational entropy
- Calculation of reduced density matrices from correlation functions
- An Area Law for One Dimensional Quantum Systems
- A class of quantum many-body states that can be efficiently simulated
- Entanglement entropy in free quantum field theory
- Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
- Jerusalem Lectures on Black Holes and Quantum Information
- Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
- The Gravity Dual of a Density Matrix
- Causality & holographic entanglement entropy
- Entanglement entropy of two disjoint intervals in conformal field theory
- Holographic Entanglement of Purification
- Holographic Entanglement Entropy
- Entanglement entropy of two disjoint intervals in conformal field theory II
- Entanglement and alpha entropies for a massive Dirac field in two dimensions
- Deriving covariant holographic entanglement
- The entanglement of purification
- Entanglement entropy of two disjoint blocks in XY chains
- Entanglement Wedge Cross Section from the Dual Density Matrix
- Derivation of holographic negativity in AdS/CFT
- Some Results on Mutual Information of Disjoint Regions in Higher Dimensions
- Entanglement Wedge Reconstruction and Entanglement of Purification
- Robustness of quantum Markov chains
- On reduced density matrices for disjoint subsystems
- Holographic Entanglement of Purification from Conformal Field Theories
- Conditional and Multipartite Entanglements of Purification and Holography
- Some Aspects of Entanglement Wedge Cross-Section
- Universal tripartite entanglement in one-dimensional many-body systems
- Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories
- Quantum Corrections to Holographic Mutual Information
- Entanglement entropy of squeezed vacua on a lattice
- Finding purifications with minimal entanglement
- Spin structures and entanglement of two disjoint intervals in conformal field theories
- Entanglement of Purification in Free Scalar Field Theories
- Pulling the Boundary into the Bulk
- Generalizations of Reflected Entropy and the Holographic Dual
- Entanglement of Purification in Many Body Systems and Symmetry Breaking
- Monogamy, polygamy, and other properties of entanglement of purification
- Mixed state entanglement measures as probe for confinement
- Entanglement of Purification in Holographic Systems
- Mutual information of excited states and relative entropy of two disjoint subsystems in CFT
- Entanglement of purification and disentanglement in CFTs
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- Balanced Partial Entanglement and Mixed State Correlations
- The Markov gap in the presence of islands
- Reflected entropy is not a correlation measure
- Holographic Study of Reflected Entropy in Anisotropic Theories
- Reflected Entropy in AdS/WCFT
- Holographic confining/deconfining gauge theories and entanglement measures with a magnetic field
- Reflected Entropy for Communicating Black Holes I: Karch-Randall Braneworlds
- Entanglement Wedge Cross Section Growth During Thermalization
- The Reflected Entanglement Spectrum for Free Fermions
- Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory
- Probing Phase Structure of Strongly Coupled Matter with Holographic Entanglement Measures
- A quantum information perspective on meson melting
- Non-Conformal Behavior of Holographic Entanglement Measures
- The Markov gap for geometric reflected entropy