  When incomplete information about the control parameters is quantified as a
prior distribution, a subtle connection emerges between quantum heat engines
and their classical analogs. We study the quantum model where the uncertain
parameters are the intrinsic energy scales and compare with the classical
models where the intermediate temperature is the uncertain parameter. The prior
distribution quantifying the incomplete information has the form $\pi(x)\propto
1/x$ in both the quantum and the classical models. The expected efficiency
calculated in near-equilibrium limit approaches the value of one third of
Carnot efficiency.
