  Realizing topological orders and topological quantum computation is a central
task of modern physics. An important but notoriously hard question in this
endeavor is how to diagnose topological orders that lack conventional order
parameters. A breakthrough in this problem is the discovery of topological
entanglement entropy, which can be used to detect nontrivial topological order
from a ground state wave function, but is far from enough for fully determining
the topological order. In this work, we take a key step further in this
direction: We propose a simple entanglement-based protocol for extracting the
quantum dimensions of all anyons from a single ground state wave function in
two dimensions. The choice of the space manifold and the ground state is
arbitrary. This protocol is both validated in the continuum and verified on
lattices, and we anticipate it to be realizable in various quantum simulation
platforms.
