Experimental Test of the Bell Inequalities

Theoretical Background

The strongest form of the Bell inequalities - the Bell-Clauser-Horne inequality - involves the measurement of coincidence and singles rates of spin components. Specifically, it involves the measurement of R++(Θ12), which is the probability of finding particle 1 in spin up with respect to angle Θ1 and particle 2 in spin up with respect to angle Θ2. This measurement is performed for 4 sets of angles, two for each detector including the four possible combinations. Furthermore the single rate R1+1) must be measured. The Bell inequality is then:

S(Θ1,Θ'12,Θ'2)=(R++(Θ'1,Θ'2) -R++12) +R++(Θ'12) +R++1,Θ'2))/ (R1+1)+ R2+2))<=1

The quantum mechanical prediction for these coincidence and singles rates can be calculated and plugged into the equation. For the case of maximum violation of Quantum Mechanics we find

S(135o,225o,0o,90o)=1/2 ηgε+(1+sqrt(2) ε2-2+ ),

where η is the detection efficiency, g is the conditional probability of finding particle 2 in detector one provided that particle 1 entered in detector 1 and ε+ and ε- are measures of the quality of the analyzers. It is clear that quantum mechanics only violates this inequality if the above mentioned parameters are as close as possible to unity. Only in this case can a test of the inequality be performed.

In all previous experiments, however, this was not the case.


Prof. Dr. Thomas Walther

Laser und Quantenoptik
Institut für Angewandte Physik
Fachbereich 05 - Physik
Technische Universität Darmstadt
Schlossgartenstr. 7
D-64289 Darmstadt

+49 6151 16-20831 (Sekretariat)

+49 6151 16-20834 (Fax)




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