  A special feature of the ground state in a topologically ordered phase is the
existence of large scale correlations depending only on the topology of the
regions. These correlations can be detected by the topological entanglement
entropy or by a measure called irreducible correlation. We show that these two
measures coincide for states obeying an area law and having zero-correlation
length. Moreover, we provide an operational meaning for these measures by
proving its equivalence to the optimal rate of a particular class of secret
sharing protocols. This establishes an information-theoretical approach to
multipartite correlations in topologically ordered systems.
