Relative entropy of excited states in conformal field theories of arbitrary dimensions

Abstract

Extending our previous work, we study the relative entropy between the reduced density matrices obtained from globally excited states in conformal field theories of arbitrary dimensions. We find a general formula in the small subsystem size limit. When one of the states is the vacuum of the CFT, our result matches with the holographic entanglement entropy computations in the corresponding bulk geometries, including AdS black branes. We also discuss the first asymmetric part of the relative entropy and comment on some implications of the results on the distinguishability of black hole microstates in AdS/CFT.

30 pages

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• Generalized entanglement entropies in two-dimensional conformal field theory
• Quantum information geometry of driven CFTs
• Local quenches, bulk entanglement entropy and a unitary Page curve
• Modular Hamiltonian for (holographic) excited states
• Bootstrapping Quantum Extremal Surfaces I: The Area Operator
• Entanglement spectrum of geometric states
• Subsystem distances between quasiparticle excited states
• Trace distance between fermionic Gaussian states from a truncation method
• Numerical calculations on the relative entanglement entropy in critical spin chains
• Quantum hypothesis testing in many-body systems
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
• Modular Hamiltonians for Euclidean Path Integral States
• Mutual information from modular flow in CFTs
• Holographic Rényi relative divergence in JT gravity