A Bell inequalities demonstration

microsansfil
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I try to understand why the correlator boundaries is −1 ≤ C(x y) ≤ 1
Hello,

In this thesis https://tel.archives-ouvertes.fr/tel-01743877/document at "1.2.2 Bell inequalities" page 7-8 it's define a correlation function :

C(x y) = P(+ + |x y) + P(− − |x y) − P(+ − |x y) − P(− + |x y), with −1 ≤ C(x y) ≤ 1.

How do one get to this relationship −1 ≤ C(x y) ≤ 1 ?

Thanks
Patrick
 
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microsansfil said:
Summary:: I try to understand why the correlator boundaries is −1 ≤ C(x y) ≤ 1

Hello,

In this thesis https://tel.archives-ouvertes.fr/tel-01743877/document at "1.2.2 Bell inequalities" page 7-8 it's define a correlation function :

C(x y) = P(+ + |x y) + P(− − |x y) − P(+ − |x y) − P(− + |x y), with −1 ≤ C(x y) ≤ 1.

How do one get to this relationship −1 ≤ C(x y) ≤ 1 ?

Thanks
Patrick
It's just a consequence of positivity $$P(\pm \pm' | xy) \geq 0$$ and normalisation $$P(++|xy) + P(+-|xy) + P(-+|xy) + P(--|xy) = 1$$ of the probabilities.
 
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