  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.
