  The second law of thermodynamics constrains that the efficiency of heat
engines, classical or quantum, cannot be greater than the universal Carnot
efficiency. We discover another bound for the efficiency of a quantum Otto heat
engine consisting of a harmonic oscillator. Dynamics of the engine is governed
by the Lindblad equation for the density matrix, which is mapped to the
Fokker-Planck equation for the quasi-probability distribution. Applying
stochastic thermodynamics to the Fokker-Planck equation system, we obtain the
$\hbar$-dependent quantum mechanical bound for the efficiency. It turns out
that the bound is tighter than the Carnot efficiency. The engine achieves the
bound in the low temperature limit where quantum effects dominate. Our work
demonstrates that quantum nature could suppress the performance of heat engines
in terms of efficiency bound, work and power output.
