A pair of spin-j particles, prepared in a singlet state, move away from each other and are examined by two distant observers. If the latter are able to discriminate between the2j+1 values of a component ofJ, there are pairs of observables whose correlation strongly violates Bell's inequality, for arbitrarily large j. However, if neighboring values are lumped together because of limited instrumental resolution, the observable correlations tend to those predicted by classical mechanics.

A hidden isospin variable is coupled to the spin of particles observed in an EPR experiment. For spin-1/2 it is shown that isospin i≥3/2 is sufficient to ensure a locally realistic spin distribution. For spin-1, examples of violation of the Mermin-Schwarz inequalities in the case of i=0 are shown satisfied with isospin. The general feature of a softening of quantum nonlocality with isospin is suggested, as well as applications to quantum physics at high energy.

A general algorithm is given for determining whether or not a given set of pair distributions allows for the construction of all the members of a specified set of higher-order distributions which return the given pair distributions as marginals. This mathematical question underlies studies of quantum correlation experiments such as those of Bell or of Clauser and Horne, or their higher-spin generalizations. The algorithm permits the analysis of rather intricate versions of such problems, in a form readily adaptable to the (...) computer. The general procedure is illustrated by simple derivations of the results of Mermin and Schwarz for the symmetric spin-1 and spin-3/2 Einstein-Podolsky-Rosen problems. It is also used to extend those results to the spin-2 and spin-5/2 cases, providing further evidence that the range of strange quantum theoretic correlations does not diminish with increasing s. The algorithm is also illustrated by giving an alternative derivation of some recent results on the necessity and sufficiency of the Clauser-Horne conditions. The mathematical formulation of the algorithm is given in general terms without specific reference to the quantum theoretic applications. (shrink)