  We investigate the charge-detection-induced dephasing of a charge qubit
interacting with an electronic beam collider composed of a quantum point
contact. We report that, while the qubit is dephased by the partitioned beam of
uncorrelated electrons, the interference of the qubit is fully restored when
the two inputs are identically biased so that all the electrons suffer
two-electron collision. This phenomenon is related to Fermi statistics and
illustrates the peculiar nonlocality of dephasing. We also describe detection
properties for the injection of entangled electron pairs.
