  Bell's inequalities are defined by sums of correlations involving
non-commuting observables in each of the two systems. Violations of Bell's
inequalities are only possible because the precision of any joint measurement
of these observables will be limited by quantum mechanical uncertainty
relations. In this paper we explore the relation between the local measurement
uncertainties and the magnitude of the correlations by preparing polarization
entangled photon pairs and performing joint measurements of non-commuting
polarization components at different uncertainty trade-offs. The change in
measurement visibility reveals the existence of a non-trivial balance between
the measurement uncertainties where the probabilities of a specific pair of
measurement outcomes approaches zero because of the particular combination of
enhancement and suppression of the experimentally observed correlations. The
occurrence of these high-contrast results shows that the quantum correlations
between the photons are close to their maximal value, confirming that the
Cirel'son bound of Bell's inequality violations is defined by the minimal
uncertainties that limit the precision of joint measurements.
