  Motivated by previous efforts in detecting topological orders from the ground
state(s) wave function, we introduce a new quantum information tool, coined the
information convex, to capture the bulk and boundary topological excitations of
a 2D topological order. Defined as a set of reduced density matrices that
minimizes the energy in a subsystem, the information convex encodes not only
the bulk anyons but also the gapped boundaries of 2D topological orders. Using
untwisted gapped boundaries of non-Abelian quantum doubles as an example, we
show how the information convex reveals and characterizes deconfined bulk and
boundary topological excitations, and the condensation rule relating them.
Interference experiments in cold atoms provide potential measurements for the
invariant structure of information convex.
