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We introduce the general class of symmetric two-qubit states guaranteeing theperfect correlation or anticorrelation of Alice and Bob outcomes whenever somespin observable is measured at both sites. We prove that, for all states fromthis class, the maximal violation of the original Bell inequality is upperbounded by 3/2 and specify the two-qubit states where this quantum upper boundis attained. The case of two-qutrit states is more complicated. Here, for alltwo-qutrit states, we obtain the same upper bound 3/2 for violation of theoriginal Bell inequality under Alice and Bob spin measurements, but we have notyet been able to show that this quantum upper bound is the least one. Wediscuss experimental consequences of our mathematical study.

Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations