  From a quantum point of view, it is mandatory to include the measurement
process when predicting the time-evolution of a quantum system. In this paper,
a model to treat the measurement of the (TeraHertz) THz electrical current in
quantum devices is presented. The explicit interaction of a quantum system with
an external measuring apparatus is analyzed through the unambiguous notion of
the Bohmian conditional wave function, the wave function of a subsystem. It it
shown that such THz quantum measurement process can be modeled as a weak
measurement: The systems suffers a small perturbation due to the apparatus, but
the current is measured with a great uncertainty. This uncertainty implies that
a new source of noise appears at THz frequencies. Numerical (quantum Monte
Carlo) experiments are performed confirming the weak character of this
measurement. This work also indicates that at low frequencies this noise is
negligible and it can be ignored. From a classical point of view, the origin of
this noise due to the measurement at THz frequencies can be attributed to the
plasmonic effect of those electrons at the contacts (by interpreting the
contacts themselves as part of the measuring apparatus).
