  As an alternative to Buttiker's dephasing lead model, we examine a dephasing
stub. Both models are phenomenological ways to introduce decoherence in chaotic
scattering by a quantum dot. The difference is that the dephasing lead opens up
the quantum dot by connecting it to an electron reservoir, while the dephasing
stub is closed at one end. Voltage fluctuations in the stub take over the
dephasing role from the reservoir. Because the quantum dot with dephasing lead
is an open system, only expectation values of the current can be forced to
vanish at low frequencies, while the outcome of an individual measurement is
not so constrained. The quantum dot with dephasing stub, in contrast, remains a
closed system with a vanishing low-frequency current at each and every
measurement. This difference is a crucial one in the context of quantum
algorithms, which are based on the outcome of individual measurements rather
than on expectation values. We demonstrate that the dephasing stub model has a
parameter range in which the voltage fluctuations are sufficiently strong to
suppress quantum interference effects, while still being sufficiently weak that
classical current fluctuations can be neglected relative to the nonequilibrium
shot noise.
