  We introduce the general class of symmetric two-qubit states guaranteeing the
perfect correlation or anticorrelation of Alice and Bob outcomes whenever some
spin observable is measured at both sites. We prove that, for all states from
this class, the maximal violation of the original Bell inequality is upper
bounded by 3/2 and specify the two-qubit states where this quantum upper bound
is attained. The case of two-qutrit states is more complicated. Here, for all
two-qutrit states, we obtain the same upper bound 3/2 for violation of the
original Bell inequality under Alice and Bob spin measurements, but we have not
yet been able to show that this quantum upper bound is the least one. We
discuss experimental consequences of our mathematical study.
