Quantum information engines: Bounds on performance metrics by measurement time

Information engines, sometimes referred to as Maxwell Demon engines, utilize information obtained through measurement to control the conversion of energy into useful work. Discussions around such devices often assume the measurement step to be instantaneous, assessing its cost by Landauer's information erasure within the measurement device. While this simplified perspective is sufficient for classical feedback-controlled engines, for nanoengines that often operate in the quantum realm, the overall performance may be significantly affected by the measurement duration (which may be comparable to the engine's cycle time) and cost (energy needed to create the system-meter correlation). In this study, we employ a generalized von Neumann measurement model to highlight that obtaining a finite amount of information requires a finite measurement time and incurs an energetic cost. We investigate the crucial role of these factors in determining the engine's performance, particularly in terms of efficiency and power output. Furthermore, for the information engine model under consideration, we establish a precise relationship between the acquired information in the measurement process and the maximum energy extractable through the measurement. We also discuss ways to extend our considerations using these concepts, such as in measurement-enhanced photochemical reactions.