Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative Entropy and Holography   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 $\Delta S=\Delta H$ for the first
order variation of the entanglement entropy $\Delta S$ and the expectation
value of the \modu Hamiltonian $\Delta H$. 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 $\Delta S=\Delta H$ for vacuum
state tomography and obtain modified versions of the Bekenstein bound.

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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: stat