Why is experimental covariance less than 1 for entangled photons?

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jk22
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Some experimental covariance curve for entangled photons gives abs(Cov(0)) less than 1.
For example : Violation of Bell inequalities by photons more than 10km apart by Gisin's group in Geneva.

Does this mean that experimentally we can't predict with certainty in this case ?

In order to explain that curve I made a quantum calculation that leads to Cov(theta) equals -7/8*cos(theta) but i find it a bit weird and don't know if i can put it in this forum.
 
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Does this mean that experimentally we can't predict with certainty in this case ?
Knowing one value, we cannot predict the other with 100% certainty in this case, right.
 
However standard qm gives -cos(theta) and hence predict with certainty at theta equals 0.

So is the theory with something to be changed in order to get nearer to the experimental result or is it the experiment which is not accurate enough ?
 
I don't know which specific experiment you mean, but no experiment is perfect. You always have uncorrelated background (or even background correlated in the wrong way), which reduces correlation.