  A wide range of experiments studying microwave photons localized in
superconducting cavities have made important contributions to our understanding
of the quantum properties of radiation. Propagating microwave photons, however,
have so far been studied much less intensely. Here we present measurements in
which we reconstruct the Wigner function of itinerant single photon Fock states
and their superposition with the vacuum using linear amplifiers and quadrature
amplitude detectors. We have developed efficient methods to separate the
detected single photon signal from the noise added by the amplifier by
analyzing the moments of the measured amplitude distribution up to 4th order.
This work is expected to enable studies of propagating microwaves in the
context of linear quantum optics.
