Quantum Process Inference for a Single Qubit Maxwell’s demon

In a quantum Maxwell’s demon experiment, two major quantities are commonly investigated -- the average work extraction 〈W〉 and the efficacy γ which measures the violation of Jarzynski’s equality when extracted information and feedback are not accounted for. Here, we carefully analyze the relation between these two quantities and find that they are not maximized simultaneously, requiring different feedback protocols. Using the tool of quantum process matrix, we are able to investigate and experimentally implement these feedback protocols.