  A charge fluctuator which is electrostatically coupled to a conducting
channel may fully dephase quantum transport through the latter. Here, we
address the case where a quantum dot (QD), playing the role of a charge
fluctuator, is tunnel-coupled to an additional channel. In the case where the
latter may support fractional charge, distinct differences from the integer
case arise: Abrupt phase lapses of the transmission through the conducting
channel occur (which may or may not be equal to $\pi$). This is accompanied by
a cusp-like suppression of the interferometer's visibility, yet no full
dephasing. We interpret our findings in terms of the entanglement between the
fluctuator and the conducting channels.
