  Bell conjectured that a positive Wigner function does not allow violation of
the inequalities imposed by local hidden variable theories. A requirement for
this conjecture is "when phase space measurements are performed". We introduce
the theory-independent concept of "operationally local transformations" which
refers to the change of the switch on a local measurement apparatus. We show
that two separated parties, performing only phase space measurements on a
composite quantum system with a positive Wigner function and performing only
operationally local transformations that preserve this positivity, can
nonetheless violate Bell's inequality. Such operationally local transformations
are realized using entangled ancillae.
