  We demonstrate that for two canonically conjugate operators $\hat{q},\hat {p}
$,the global correlation $\langle \hat{q} \hat {p} + \hat{p} \hat {q} \rangle
-2 \langle \hat{q}\rangle \langle \hat {p}\rangle$, and the local correlations
$\langle \hat{q} \rangle (p) - \langle \hat{q}\rangle$ and $\langle \hat{p}
\rangle (q)-\langle \hat {p}\rangle$ can be measured exactly by Von
Neumann-Arthurs-Kelly joint quadrature measurements . These correlations
provide a sensitive experimental test of quantum phase space probabilities
quite distinct from the probability densities of $ q,p $. E.g. for EPR states,
and entangled generalized coherent states, phase space probabilities which
reproduce the correct position and momentum probability densities have to be
modified to reproduce these correlations as well.
