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Localization of Negative Energy and the Bekenstein Bound
A simple argument shows that negative energy cannot be isolated far away from
positive energy in a conformal field theory and strongly constrains its
possible dispersal. This is also required by consistency with the Bekenstein
bound written in terms of the positivity of relative entropy. We prove a new
form of the Bekenstein bound based on the monotonicity of the relative entropy,
involving a "free" entropy enclosed in a region which is highly insensitive to
space-time entanglement, and show that it further improves the negative energy
localization bound.Comment: 5 pages, 1 figur
ETFS : una fórmula de inversión al alcance de todos
Universidad de Sevilla. Grado en Finanzas y Contabilida
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 for the first
order variation of the entanglement entropy and the expectation
value of the \modu Hamiltonian . 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 for vacuum
state tomography and obtain modified versions of the Bekenstein bound.Comment: 75 pages, 3 figures, added reference
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