Holographic Mutual Information is Monogamous

TL;DR

This paper demonstrates that holographic quantum field theories exhibit a monogamy property of mutual information, indicating that their correlations are predominantly quantum entanglement rather than classical, and confirms the Ryu-Takayanagi formula's consistency with entanglement entropy inequalities.

Contribution

It establishes a monogamy inequality for mutual information in holographic theories and verifies the Ryu-Takayanagi formula's compatibility with known entanglement entropy inequalities.

Findings

Mutual information in holographic theories obeys monogamy relations.

The Ryu-Takayanagi formula is consistent with all known entanglement entropy inequalities.

Supports the view that holographic correlations are mainly quantum entanglement.

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.