Abstract
We formulate a quantum master equation for the many-particle density matrix of electrons propagating through a single-mode conductor, combining elastic scattering by disorder with time-resolved projective measurements that monitor the outcome of scattering events. The full counting statistics of transmitted electrons has a binomial distribution function, whose mean T and variance T(1- T) determine the conductance and shot noise power, respectively. Monitoring suppresses the phase coherence responsible for one-dimensional localization: The decay with conductor length L of the typical transmission probability crosses over at L≃ ℓ_φ from the exponential e^-L/ξ (with localization length ξ) to the Ohmic 1/L decay. Numerical solution of the master equation gives, for weak monitoring, a logarithmic dependence ℓ_φ≃ ξln(v_ Fτ_φ/ξ) of the coherence length ℓ_φ on the mean time τ_φ between measurements.