Title: Maxwell's two-demon engine under pure dephasing noise

Abstract: The interplay between thermal machines and quantum correlations is of great interest in both quantum thermodynamics and quantum information science. Recently, a quantum Szil\'ard engine has been proposed, showing that the quantum steerability between a Maxwell's demon and a work medium can be beneficial to a work extraction task. Nevertheless, this type of quantum-fueled machine is usually fragile in the presence of decoherence effects. We provide an example of the pure dephasing process, showing that the engine's quantumness can be degraded. Therefore, in this work, we tackle this question by introducing a second demon who can access a control system and make the work medium pass through two dephasing channels in a manner of quantum superposition. Furthermore, we provide a quantum circuit to simulate our proposed concept and test it on IBMQ and IonQ quantum computers.