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Recent progress in the development of superconducting circuits has enabledthe realization of interesting sources of nonclassical radiation at microwavefrequencies. Here, we discuss field quadrature detection schemes for theexperimental characterization of itinerant microwave photon fields and theirentanglement correlations with stationary qubits. In particular, we presentjoint state tomography methods of a radiation field mode and a two-levelsystem. Including the case of finite quantum detection efficiency, we relatemeasured photon field statistics to generalized quasi-probability distributionsand statistical moments for one-channel and two-channel detection. We alsopresent maximum-likelihood methods to reconstruct density matrices frommeasured field quadrature histograms. Our theoretical investigations aresupported by the presentation of experimental data, for which microwave quantumfields beyond the single-photon and Gaussian level have been prepared andreconstructed.

Characterizing Quantum Microwave Radiation and its Entanglement with Superconducting Qubits using Linear Detectors