An entanglement band structure for general multiqubit states

Majorana drew a symmetric multiqubit state as points on the Bloch sphere, antipodal to the zeros of its overlap with spin coherent states. Projecting only one qubit of a general state leaves the others in a state that varies with direction. Its entanglement invariants are eigenvalues of a non-Hermitian matrix and form bands over the sphere. Exceptional points appear, without gain or loss, where the entanglement family of the rest changes. Circling one exchanges two bands, so the bands form one Riemann surface. At five qubits it fixes the entanglement class up to finitely many choices.