  Entangled states can help in quantum state discrimination by local operations
and classical communication (LOCC). For example, a Bell state is necessary (and
sufficient) to perfectly discriminate a set of either three or four Bell states
by LOCC. In this paper, we consider the task of LOCC discrimination of the
states of noisy Bell ensembles, where a given ensemble consists of the states
obtained by mixing the Bell states with an arbitrary two-qubit state with
nonzero probabilities. It is proved that a Bell state is required for optimal
discrimination by LOCC, even though the ensembles do not contain, in general,
any maximally entangled state, and in specific instances, any entangled state.
