2014/04/30 by Nima Lashkari · 101 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Entropy (arrow of time) #Entropy in thermodynamics and information theory #Generalized relative entropy #Joint entropy #Joint quantum entropy #Kullback–Leibler divergence #Mathematical analysis #Mathematics #Maximum entropy thermodynamics #Physics #Principle of maximum entropy #Quantum #Quantum discord #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum relative entropy #Quantum state #Rényi entropy #Statistical physics #Statistics #Trace distance #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevlett.113.051602
published in Physical Review Letters 113(5), 051602 (American Physical Society)
arxiv created 2014/06/23 · openalex publication_date 2014/07/29 · arxiv updated 2014/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance.