  The first global quantum simulation of semiconductor-based quantum-cascade
lasers is presented. Our three-dimensional approach allows to study in a purely
microscopic way the current-voltage characteristics of state-of-the-art
unipolar nanostructures, and therefore to answer the long-standing
controversial question: is charge transport in quantum-cascade lasers mainly
coherent or incoherent? Our analysis shows that: (i) Quantum corrections to the
semiclassical scenario are minor; (ii) Inclusion of carrier-phonon and
carrier-carrier scattering gives excellent agreement with experimental results.
