Simple Test for Hidden Variables in Spin-1 Systems

We resolve an old problem about the existence of hidden parameters in a three-dimensional quantum system by constructing an appropriate Bell’s type inequality. This reveals the nonclassical nature of most spin-1 states. We shortly discuss some physical implications and an underlying cause of this nonclassical behavior, as well as a perspective of its experimental verification.

Figure 1

Regular pentagram defined by cyclic quintuplet of unit vectors ${\ell }_i\perp {\ell }_{i+1}$. State vector $|\psi ⟩$ is directed along the symmetry axis of the pentagram.