The Holographic Entropy Cone

Understand

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries.

• For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities.
• This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions.
• We also find an infinite new family of inequalities applicable to 5 or more regions.