Symmetries and entanglement of stabilizer states

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, invertible (unitary and nonunitary) 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. More precisely, we study a central problem in entanglement theory, which is
concerned with the existence of transformations via local operations among pure states.We demonstrate that the
identified symmetries enable additional transformations from a stabilizer state to some other multipartite pure
state. Furthermore, we demonstrate how the identified symmetries can be used to construct stabilizer codes with
diagonal transversal gates.