Holographic Mutual Information is Monogamous

TL;DR

The paper shows that holographic theories obey a monogamy relation for mutual information, I3 ≤ 0, under the Ryu-Takayanagi entanglement entropy prescription.It provides a geometric proof based on rearranging RT minimal surfaces and extends the result to higher-curvature corrections and general large-N theories with classical bulk dynamics.The authors demonstrate that this monogamy is a strong consistency check for RT and suggests that correlations in holographic theories are dominated by entanglement rather than classical correlations.They connect monogamy to broader entanglement-entropy inequalities and discuss implications for the structure of correlations, absence of quantum Markov chains, and cryptographic interpretations, while outlining open questions and finite-N corrections.

Abstract

We identify a special information-theoretic property of quantum field theories with holographic duals: the mutual informations among arbitrary disjoint spatial regions A,B,C obey the inequality I(A:BC) >= I(A:B)+I(A:C), provided entanglement entropies are given by the Ryu-Takayanagi formula. Inequalities of this type are known as monogamy relations and are characteristic of measures of quantum entanglement. This suggests that correlations in holographic theories arise primarily from entanglement rather than classical correlations. We also show that the Ryu-Takayanagi formula is consistent with all known general inequalities obeyed by the entanglement entropy, including an infinite set recently discovered by Cadney, Linden, and Winter; this constitutes strong evidence in favour of its validity.