  In order to describe quantum heat engines, here we systematically study
isothermal and isochoric processes for quantum thermodynamic cycles. Based on
these results the quantum versions of both the Carnot heat engine and the Otto
heat engine are defined without ambiguities. We also study the properties of
quantum Carnot and Otto heat engines in comparison with their classical
counterparts. Relations and mappings between these two quantum heat engines are
also investigated by considering their respective quantum thermodynamic
processes. In addition, we discuss the role of Maxwell's demon in quantum
thermodynamic cycles. We find that there is no violation of the second law,
even in the existence of such a demon, when the demon is included correctly as
part of the working substance of the heat engine.
