REMARKS ON BELL'S INEQUALITY FOR SPIN CORRELATIONS

where ei,^2,..., en are ?1. It is not difficult to construct real non-negative definite matrices E = ((crij)), 1 5! hj 5: n, satisfying an = 1 for every i but not (1.1). Thus there arises the natural problem of finding simple verifiable conditions on E in order to ensure that it is the correlation matrix of n spin variables. Here we shall find such necessary and sufficient conditions when n = 3 or 4. We also obtain a characterisation of all correlation matrices of n exchangeable spin variables. By using the observables of a fermion field obeying the canonical anticom mutation relations it is possible to realize any non-negative matrix with diagonal entries unity as the correlation matrix of spin observables.