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Classicality of spin states

Olivier Giraud, Petr Braun, and Daniel Braun

We extend the concept of classicality in quantum optics to spin states.We call a state “classical” if its density matrix can be decomposed as a weighted sum of angular momentum coherent states with positive weights. Classical spin states form a convex set C, which we fully characterize for a spin 1/2 and a spin 1. For arbitrary spin, we provide “nonclassicality witnesses.” For bipartite systems, C forms a subset of all separable states. A state of two spins 1/2 belongs to C if and only if it is separable, whereas for a spin 1/2 coupled to a spin 1, there are separable states which do not belong to C. We show that in general the question whether a state is in C can be answered by a linear programming algorithm.