Holographic entropy inequalities pass the majorization test

TL;DR

This paper proves a key property of holographic entropy inequalities, showing that systems with overlapping regions on one side are contained within certain systems on the other side, supporting their validity in dynamic conditions.

Contribution

It establishes a new subsumption property of holographic entropy inequalities, strengthening their theoretical foundation and implications for quantum information and gravity.

Findings

Proved a conjectured subsumption property of entropy inequalities.

Showed inequalities constrain entropies in time-dependent scenarios.

Commented on links to quantum erasure correction and RG flow.

Abstract

Quantities computed by minimal cuts, such as entanglement entropies achievable by the Ryu-Takayanagi proposal in the AdS/CFT correspondence, are constrained by linear inequalities. We prove a previously conjectured property of all such constraints: Any $k$ systems on the "greater-than" side of the inequality whose overlap is nonempty are subsumed in some $k$ systems on its "less-than" side (accounting for multiplicity). This finding adds evidence that the same inequalities also constrain the entropies under time-dependent conditions because it preempts a large class of potential counterexamples. We prove several other properties of holographic entropy inequalities and comment on their relation to quantum erasure correction and the Renormalization Group.