Classicality of spin states
Olivier Giraud, Petr A. Braun, Daniel Braun · Physical Review A · 2008
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 $\mathcal{C}$, which we fully characterize for a spin $1∕2$ and a spin 1. For arbitrary spin, we provide ``nonclassicality witnesses.'' For bipartite systems, $\mathcal{C}$ forms a subset of all separable states. A state of two spins $1∕2$ belongs to $\mathcal{C}$ 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 $\mathcal{C}$. We show that in general the question whether a state is in $\mathcal{C}$ can be answered by a linear programming algorithm.