Classicality of spin states

Olivier Giraud (1) , Petr Braun (2, 3) , Daniel Braun (1)

1 ICQ - Cohérence Quantique (LPT)
2 Institute of Physics [Saint-Petersburg]
3 Fachbereich Physik [Duisburg]

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 ''non-classicality 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.

Domaines: Physique Quantique [quant-ph]

Olivier Giraud, Petr Braun, Daniel Braun. Classicality of spin states. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2008, 78 (4), pp.042112. ⟨10.1103/PhysRevA.78.042112⟩. ⟨hal-00344145⟩