# If quantum entanglement causes the violations of Bell's inequality why don't we see perfect correlation?

From wikipedia:

For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be counterclockwise.

Yet the Bell tests all observe a lesser correlation:

If S is numerically greater than 2 it has infringed the CHSH inequality. The experiment is declared to have supported the QM prediction and ruled out all local hidden variable theories.

Is there any way to run an experiment that could observe (near) perfect correlation?

No. Tsirelson's bound states that, e.g., the value of $$2\sqrt{2}$$ obtained for the CHSH inequality is optimal within quantum theory, while the maximum value obtainable within all theories which cannot communicate instantly (no-signalling theories) would be 4.