Abstract
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.
Highlights
Violations of Bell’s inequalities demonstrate that conventional quantum mechanics is incompatible with local realism [1]
We have investigated the relation between the measurement uncertainties of joint measurements and the non-local correlations responsible for the violation of Bell’s inequalities by experimentally observing the joint probabilities of the four outcomes xA, yA, xB, and yB that appear in the formulation of Bell’s inequalities for an input state that maximally violates the corresponding Bell’s inequality
By varying the uncertainty trade-off in our measurements we have identified the maximal sensitivity of experimentally observed outcome probabilities to the total correlation | B | that appears in Bell’s inequalities
Summary
Violations of Bell’s inequalities demonstrate that conventional quantum mechanics is incompatible with local realism [1]. Experimental violations of Bell’s inequalities were first observed in optical experiments performed in the 1980s [2], followed by a number of refinements of the methods resulting in an increasingly reliable confirmation of the essential result [3, 4, 5, 6, 7, 8, 9, 10, 11] These experimental results all confirm the validity of the mathematical formalism without explaining the physical mechanism associated with the failure of local realism [12]. The closest approximation of a joint non-contextual reality of non-commuting observables is an uncertainty limited joint measurement of the two observables This means that there must be a quantitative relation between the maximal permitted violation of a Bell’s inequality given by the Cirel’son bound [30] and the uncertainty limit of joint measurements. It may be interesting to study the characteristics of the non-classical correlations responsible for a maximal violation of a Bell’s inequality using the experimentally observable statistics of uncertainty limited joint measurements
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