  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.
