Quantum Extremal Surfaces and the Holographic Entropy Cone

TL;DR

This paper explores how quantum corrections via the Quantum Extremal Surface (QES) influence the holographic entropy cone, showing that bulk entropy constraints like the Holographic Entropy Cone (HEC) and monogamy of mutual information (MMI) are preserved at the boundary.

Contribution

It establishes a connection between bulk entropy constraints and boundary entropy inequalities within the QES framework, extending the understanding of holographic entropies.

Findings

Bulk HEC implies boundary HEC.

Bulk MMI implies boundary MMI.

Quantum corrections preserve key entropy inequalities.

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.