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If there exist a non-local variable that determine the result of the pair of result, then one gets for result of measurement [tex]0, 4, -4[/tex]

Whereas in quantum mechanics, the total Bell operator is [tex]\frac{1}{\sqrt{2}}\left(\begin{array}{cc} 2 &0&0&2\\0&-2&2&0\\0&2&-2&0\\2&0&0&2\end{array}\right)[/tex] which has as possible measurement outcomes : [tex]0, 2\sqrt{2},-2\sqrt{2}[/tex] which are not the same as the one given by a nonlocal variable since the eigenvalue of a sum of operator is not equal to the sum of the eigenvalues.

Since the measurement outcomes are not the same, does this indicates that there can be no non-local variable can exist ?