  We develop a framework for the derivation of new information theoretic
quantities which are natural from a holographic perspective. We demonstrate the
utility of our techniques by deriving the tripartite information (the quantity
associated to monogamy of mutual information) using a set of abstract arguments
involving bulk extremal surfaces. Our arguments rely on formal manipulations of
surfaces and not on local surgery or explicit computation of entropies through
the holographic entanglement entropy prescriptions. As an application, we show
how to derive a family of similar information quantities for an arbitrary
number of parties. The present work establishes the foundation of a broader
program that aims at the understanding of the entanglement structures of
geometric states for an arbitrary number of parties. We stress that our method
is completely democratic with respect to bulk geometries and is equally valid
in static and dynamical situations. While rooted in holography, we expect that
our construction will provide a useful characterization of multipartite
correlations in quantum field theories.
