Quantum state reconstruction and detection of quantum coherences on different observation levels

We apply the Jaynes principle of maximum entropy [Phys. Rev. 106, 620 (1957); 108, 171 (1957)] for a reconstruction of Wigner functions of quantum-mechanical states of light on different observation levels. We study how quantum interference between components of superpositions of coherent states, which is responsible for the appearance of nonclassical effects, can be detected on different observation levels. We analyze in detail the reconstruction of Wigner functions of squeezed states on different observation levels in the case of nonunit detection efficiency modeled as a decay of the state under consideration into a zero-temperature reservoir.