Effects of Entanglement in Controlled Dephasing

In controlled dephasing as a result of the interaction of a controlled environment (dephasor) and the system under observation (dephasee) the states of the two subsystems are entangled. Using as an example the ``Which Path Detector'', we discuss how the entanglement influences the controlled dephasing. In particular, we calculate the suppression $\nu$ of A-B oscillations as a function of the bias $eV$ applied to the QPC and the coupling $\Gamma$ of the QD to the leads. At low temperatures the entanglement produces a smooth crossover from $\nu \propto (eV/\Gamma)^2$, when $eV \ll \Gamma$ to $\nu \propto eV/\Gamma$, for $eV \gg \Gamma$.