Two-dimensional Planck spectroscopy for microwave photon calibration

Quantum state tomography of weak microwave signals is an important part of many protocols in the field of quantum information processing with superconducting circuits. This step typically relies on an accurate $\textit{in-situ}$ estimation of signal losses in the experimental set-up and requires a careful photon number calibration. Here, we present an improved method for the microwave loss estimation inside of a closed cryogenic system. Our approach is based on Planck's law and makes use of independent temperature sweeps of individual parts of the cryogenic set-up. Using this technique, we can experimentally resolve changes in microwave losses of less than 0.1 dB in the cryogenic environment. We discuss potential applications of this approach for precise characterization of quantum-limited superconducting amplifiers and in other prominent experimental settings.