Quantumness beyond entanglement: The case of symmetric states

Abstract

Nowadays, it is 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 state from entangled to separable, and vice versa. We propose to certify the presence of quantumness via an average of a state's bipartite entanglement properties 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.