Tomography from Entanglement

Abstract

The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. We also show that positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the conformal field theory, follow from positivity conditions on the bulk matter energy density. We discuss an information theoretical interpretation of the convexity in terms of the Fisher metric.

6 pages

References in corpus (5)

• Towards a derivation of holographic entanglement entropy
• Thermodynamical Property of Entanglement Entropy for Excited States
• Nuts and Bolts for Creating Space
• Covariant Residual Entropy
• Nonlinear constraints on gravity from entanglement

Cited by in corpus (8)

• Relative entropy of excited states in conformal field theories of arbitrary dimensions
• Equivalent Equations of Motion for Gravity and Entropy
• Kinematic space for conical defects
• Explicit reconstruction of the entanglement wedge
• Integral Geometry and Holography
• Inviolable energy conditions from entanglement inequalities
• Generalized geodesic deviation equations and an entanglement first law for rotating BTZ black holes
• Numerical calculations on the relative entanglement entropy in critical spin chains