Self-calibration for self-consistent tomography

Self-calibrating states are introduced as quantum resources for the simultaneous reconstruction of a quantum state and measurement device. Simple criteria for a state being self-calibrating are formulated. Theory applies to realistic state estimation scenarios, where the detection model is nonlinear in unknown parameters of the measuring device. Examples discussed include time multiplexed detection with on/off detectors and quantum homodyne tomography. The thermally noised single-photon states and Gaussian states are self-calibrating for these schemes. For homodyne tomography, statistical tests applied to raw measured data are sufficient for judging whether or not the signal state is self-calibrating without any a priori information.