The CHSH inequality, named for Clauser, Horne, Shimony, and Holt (1969), is a Bell inequality involving two measurement choices
at each of two locations. Let 
, 
, 
, and 
be random variables taking
values in 
on one probability space, and put 
,
where the brackets denote expectation values.
Then
 |
Indeed, the pointwise expression
 |
has absolute value 2, since precisely one of 
and 
is zero. Taking its expectation
value proves the bound.
The common probability space is essential: the four pairwise correlations must be compatible with one joint distribution. Quantum measurement correlations need not satisfy this requirement and can violate the bound.
