Relative entropy and holography

DOI10.1007/JHEP08(2013)060zbMATH Open1342.83128arXiv1305.3182OpenAlexW3098062506MaRDI QIDQ737472

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Publication date: 12 August 2016

Published in: (Search for Journal in Brave)

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 $DeltaS=DeltaH$ for the first order variation of the entanglement entropy $DeltaS$ and the expectation value of the modu Hamiltonian $DeltaH$. 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 $DeltaS=DeltaH$ for vacuum state tomography and obtain modified versions of the Bekenstein bound.

Full work available at URL: https://arxiv.org/abs/1305.3182

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