Long-distance entanglement of purification and reflected entropy in conformal field theory

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.

5 pages, 2 figures + appendices; v2: previous results unchanged, added proof of the long-distance behaviour of EoP, reorganized presentation

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Cited by in corpus (14)

• 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${}_3$/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