Anticoherent spin-2 states and spherical designs

Anticoherent spin states are introduced as quantum states that exhibit maximally nonclassical behaviors which are important in the study of quantum entanglement. Using Majorana representation of spin states, Crann-Pereira-Kribs studied the relation between anticoherent spin states and spherical designs. They proposed a conjecture that a spin-s state is anticoherent to order t if and only if its Majorana representation is a spherical t-design on S (2). In this paper, we prove that this conjecture is true for s = 2.