  We point out that, when the dimension of the Hilbert space is greater than
two, Bell's operators entering the Bell-CHSH inequality exhibit unitarily
inequivalent representations. Although the Bell-CHSH inequality turns out to be
violated, the size of the violation is different for different representations,
the maximum violation being given by Tsirelson's bound. The feature relies on a
pairing mechanism between the modes of the Hilbert space of the system.
