Symmetric states: local unitary equivalence via stabilizers

Understand

We classify local unitary equivalence classes of symmetric states via a classification of their local unitary stabilizer subgroups.

• For states whose local unitary stabilizer groups have a positive number of continuous degrees of freedom, the classification is exhaustive.
• We show that local unitary stabilizer groups with no continuous degrees of freedom are isomorphic to finite subgroups of the rotation group SO(3), and give examples of states with discrete stabilizers.