Two aspects of the Clauser-Horne conditions for the compatibility with local realism of measured spin-½ Einstein-Podolsky-Rosen correlations are investigated in the spin-$s$ case. (1) A new set of necessary conditions is given for compatibility with local realism. These conditions are violated for a large range of geometries. The range does not diminish with increasing $s$, if the observed correlations are sufficiently near to the quantum-theoretic predictions. (2) A simple counterexample is given to the spin-1 generalization of a recent conjecture that the conditions tested by the Clauser-Horne spin-½ inequalities are sufficient as well as necessary for compatibility of the data with local realism.

• Received 9 July 1982

DOI:https://doi.org/10.1103/PhysRevD.27.339