  Stabilizer states constitute a set of pure states which plays a dominant role
in quantum error correction, measurement--based quantum computation, and
quantum communication. Central in these applications are the local symmetries
of these states. We characterize all local symmetries of arbitrary stabilizer
states and provide an algorithm which determines them. We demonstrate the
usefulness of these results by showing that the additional local symmetries
find applications in entanglement theory and quantum error correction.
