Characterizing Quantum Microwave Radiation and its Entanglement with Superconducting Qubits

Recent progress in the development of superconducting circuits has allowed for realizing interesting sources of nonclassical radiation at microwave frequencies. Here, we discuss field quadrature detection schemes for the experimental characterization of itinerant microwave photon fields and their entanglement correlations with stationary qubits. In particular, we present joint state tomography methods of a radiation field mode and a two-level system. Including the case of finite quantum detection efficiency, we relate measured photon field statistics to generalized quasi-probability distributions and statistical moments. We also present maximum-likelihood methods to reconstruct density matrices from measured field quadrature histograms.

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