  Pulsed homodyne quantum tomography usually requires a high detection
efficiency limiting its applicability in quantum optics. Here, it is shown that
the presence of low detection efficiency ($<50\%$) does not prevent the
tomographic reconstruction of quantum states of light, specifically, of
Gaussian type. This result is obtained by applying the so-called "minimax"
adaptive reconstruction of the Wigner function to pulsed homodyne detection. In
particular, we prove, by both numerical and real experiments, that an effective
discrimination of different Gaussian quantum states can be achieved. Our
finding paves the way to a more extensive use of quantum tomographic methods,
even in physical situations in which high detection efficiency is unattainable.

Optics;Quantum Physics