Relative entropy and holography

A bstract Relative entropy between two states in the same Hilbert space is a fundamental statistical measure of the distance between these states. Relative entropy is always positive and increasing with the system size. Interestingly, for two states which are infinitesimally different to each other,...

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Bibliographic Details
Published in:The journal of high energy physics 2013-08, Vol.2013 (8), p.1-65, Article 60
Main Authors: Blanco, David D., Casini, Horacio, Hung, Ling-Yan, Myers, Robert C.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Elementary Particles
Entanglement
Entropy
High energy physics
Hilbert space
Holography
Inequalities
Mathematical analysis
Modular
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
String Theory
Tomography
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Summary:A bstract Relative entropy between two states in the same Hilbert space is a fundamental statistical measure of the distance between these states. Relative entropy is always positive and increasing with the system size. Interestingly, for two states which are infinitesimally different to each other, vanishing of relative entropy gives a powerful equation Δ S = Δ H for the first order variation of the entanglement entropy Δ S and the expectation value of the modular Hamiltonian Δ H . We evaluate relative entropy between the vacuum and other states for spherical regions in the AdS/CFT framework. We check that the relevant equations and inequalities hold for a large class of states, giving a strong support to the holographic entropy formula. We elaborate on potential uses of the equation Δ S = Δ H for vacuum state tomography and obtain modified versions of the Bekenstein bound.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP08(2013)060