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Relative entropy and holography

  • David D. Blanco
  • Horacio Casini
  • Ling-Yan Hung
  • Robert C. Myers
Article

Abstract

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 ΔS = ΔH for the first order variation of the entanglement entropy ΔS and the expectation value of the modular Hamiltonian ΔH. 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 ΔS = ΔH for vacuum state tomography and obtain modified versions of the Bekenstein bound.

Keywords

AdS-CFT Correspondence Black Holes Holography and condensed matter physics (AdS/CMT) 

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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • David D. Blanco
    • 1
  • Horacio Casini
    • 1
  • Ling-Yan Hung
    • 2
  • Robert C. Myers
    • 3
  1. 1.Centro Atómico BarilocheS.C. de BarilocheArgentina
  2. 2.Department of PhysicsHarvard UniversityCambridgeU.S.A.
  3. 3.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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