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Summary form only given. Summary from only given. The canonical correlation, which describes the fundamental correlation between two separated subsystems S/sub 1/ and S/sub 2/, is described by the Schmidt decomposition. Using information theory, we find that hidden variables theories lead to a refined distribution where the original values of P/sub i/ and P/sub j/ have been resolved into a number of values P/sub i/spl lambda// and P/sub j/spl lambda//. Following a calculation which includes hidden variables, the following interesting result has been found: I/sub Shann//sup HV/=I/sub c/. This result means that the refinement by hidden variables should increase the amount of information included in the Shannon index of correlation, so that it can be equal to the quantum index of correlation. We find that hidden variable theories lead to mutual information between subsystems which is larger than that obtained by QM. A by-product of refuting the hidden variables theories is reestablishing the quantum limit of mutual information. However, following the last equality a possible unconventional meaning to hidden variables is discussed.