  Joint quantum measurements of non-commuting observables are possible, if one
accepts an increase in the measured variances. A necessary condition for a
joint measurement to be possible is that a joint probability distribution
exists for the measurement. This fact suggests that there may be a link with
Bell inequalities, as these will be satisfied if and only if a joint
probability distribution for all involved observables exists. We investigate
the connections between Bell inequalities and conditions for joint quantum
measurements to be possible. Mermin's inequality for the three-particle
Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition
for a joint measurement on two out of the three quantum systems to exist.
Gisin's Bell inequality for three co-planar measurement directions, meanwhile,
is shown to be less strict than the condition for the corresponding joint
measurement.
