Quantum process inference for a single qubit Maxwell's demon

While quantum measurement theories are built around density matrices and observables, the laws of thermodynamics are based on processes such as are used in heat engines and refrigerators. The study of quantum thermodynamics fuses these two distinct paradigms. In this article, we highlight the usage of quantum process matrices as a unified language for describing thermodynamic processes in the quantum regime. We experimentally demonstrate this in the context of a quantum Maxwell's demon, where two major quantities are commonly investigated; the average work extraction $\langle W \rangle$ and the efficacy $\gamma$ which measures how efficiently the feedback operation uses the obtained information. Using the tool of quantum process matrices, we develop the optimal feedback protocols for these two quantities and experimentally investigate them in a superconducting circuit QED setup.