  It is nowadays accepted that truly quantum correlations can exist even in the
absence of entanglement. For the case of symmetric states, a physically trivial
unitary transformation can alter a quantum state from entangled to separable
and vice versa. We propose to certify the presence of quantumness via an
average over all physically relevant modal decompositions. We investigate
extremal states for such a measure: SU(2)-coherent states possess the least
quantumness whereas the opposite extreme is inhabited by states with maximally
spread Majorana constellations.
