  We consider dephasing in the electronic Mach-Zehnder interferometer strongly
coupled to current noise created by a voltage biased quantum point contact
(QPC). We find the visibility of Aharonov-Bohm oscillations as a function
voltage bias and express it via the cumulant generating function of noise. In
the large-bias regime, high-order cumulants of current add up to cancel the
dilution effect of a QPC. This leads to an abrupt change in the dependence of
the visibility on voltage bias which occurs at the QPC's transparency T=1/2.
Quantum fluctuations in the vicinity of this point smear out the sharp
transition.
