Some new, powerful, and very simple Bell inequalities are derived. They establish that for two spin-$s$ particles in the singlet state, the quantum-theoretic Einstein-Podolsky-Rosen correlations for spin measurements along all pairs of directions from a set of $N$ axes are incompatible with local realism for any set of distinct coplanar axes when $N=3\mathrm{}$, and for any set of distinct axes whatever when $N=4\mathrm{}$, with the possible exception of sets restricted by one of the constraints $\hat{a}\pm \hat{b}\pm \hat{c}\pm \hat{d}=0\mathrm{}$. These results hold for any value of the spin.

• Received 17 June 1982

DOI:https://doi.org/10.1103/PhysRevLett.49.901