Abstract
Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the Ryu-Takayanagi (RT) formula defines the Holographic Entropy Cone (HEC). These inequalities are no longer satisfied once general quantum corrections are included by employing the Quantum Extremal Surface (QES) prescription. Nevertheless, the structure of the QES formula allows for a controlled study of how quantum contributions from bulk entropies interplay with HEC inequalities. In this paper, we initiate an exploration of this problem by relating bulk entropy constraints to boundary entropy inequalities. In particular, we show that requiring the bulk entropies to satisfy the HEC implies that the boundary entropies also satisfy the HEC. Further, we also show that requiring the bulk entropies to obey monogamy of mutual information (MMI) implies the boundary entropies also obey MMI.
Highlights
JHEP11(2021)177 sub-class of all quantum states, satisfying certain additional constraints
The exploration of holographic entropy inequalities had focused on using the RT formula and its geometric nature
We have learned in the past few years that quantum effects incorporated using the Quantum Extremal Surface (QES) formula can play a crucial role, e.g., in the presence of black holes
Summary
We motivate our first result, namely, the fact that the bulk HEC implies the boundary HEC. We have exemplified how the usual constructs for holographic entropy inequalities can be applied to both bulk and boundary entropies in a coordinated way in the setting of double holography Within this framework, it becomes clear that the bulk HEC holds (by double holography) and so does the boundary HEC (because island contributions do not spoil the usual cut-and-paste arguments). It is plausible that requiring the bulk HEC to hold for arbitrary subregions (including those on the brane), could imply the existence of a higher-dimensional geometric description where the entropies are computed using the RT formula.. It is plausible that requiring the bulk HEC to hold for arbitrary subregions (including those on the brane), could imply the existence of a higher-dimensional geometric description where the entropies are computed using the RT formula.7 This in turn would imply the boundary HEC by using the corresponding doubly holographic picture. We elucidate a more direct mechanism by which the bulk HEC implies the boundary HEC in full generality
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