Symmetric entanglement classes for n qubits

Abstract: Permutation-symmetric n qubit pure states can be represented by n points on the surface of the unit sphere by means of the Majorana representation. Here this representation is employed to characterize and compare the three entanglement classification schemes LOCC, SLOCC and the Degeneracy Configuration. Symmetric SLOCC operations are found to be described by Mobius transformations, and an intuitive visualization of their freedoms is presented. For symmetric states of up to 5 qubits explicit forms of representative states for all SLOCC classes are derived. The symmetric 4 qubit entanglement classes are compared to the entanglement families introduced in [PRA 65, 052112 (2002)], and examples are given how the SLOCC-inequivalence of symmetric states can be quickly determined from known results about Mobius transformations.