Abstract
Quantum states of a spin 1/2 (a qubit) are parametrized by the space CP¹ ∼ S², the Bloch sphere. A spin j for a generic j (a 2j+1-state system) is represented instead by a point of a larger space, CP^2j. Here we study the state of a single angular momentum/spin in the limit, j → ∞. The special class of states | j, n ∈ CP^2j , with spin oriented towards definite spatial directions n ∈ S², i.e., (J· n ) | j, n = j |j, n , are found to behave as classical angular momenta, j n, in this limit. Vice versa, general spin states in CP^2j do not become classical, even at large j. We discuss these questions, by analysing the Stern-Gerlach processes, the angular-momentum composition rule, and the rotation matrix. Our observations help to clarify better how classical mechanics emerges from quantum mechanics in this context (e.g., with unique trajectories for a particle carrying a large spin), and to make the widespread idea that large spins somehow become classical, more precise.