  We propose a dynamical scheme for measuring the full counting statistics in a
mesoscopic conductor using an electronic Mach-Zehnder interferometer. The
conductor couples capacitively to one arm of the interferometer and causes a
phase shift which is proportional to the number of transferred charges.
Importantly, the full counting statistics can be obtained from average current
measurements at the outputs of the interferometer. The counting field can be
controlled by varying the time delay between two separate voltage signals
applied to the conductor and the interferometer, respectively. As a specific
application we consider measuring the entanglement entropy generated by
partitioning electrons on a quantum point contact. Our scheme is robust against
moderate environmental dephasing and can be realized thanks to recent advances
in giga-hertz quantum electronics.
