Explain the concept of topological entanglement entropy and its role in identifying topologically ordered phases in quantum systems.

Topological entanglement entropy is a measure that captures the long-range entanglement in topologically ordered phases. It is defined as the constant term in the scaling of entanglement entropy with subsystem size, distinguishing it from short-range entanglement present in conventional phases. This measure is robust against local perturbations and provides a signature of topological order, revealing information about the underlying anyonic excitations and ground state degeneracy in systems like fractional quantum Hall states and spin liquids.