  We consider the efficiency at maximum power of a quantum Otto engine, which
uses a spin or a harmonic system as its working substance and works between two
heat reservoirs at constant temperatures $T_h$ and $T_c$ $ (<T_h)$. Although
the spin-$1/2$ system behaves quite differently from the harmonic system in
that they obey two typical quantum statistics, the efficiencies at maximum
power based on these two different kinds of quantum systems are bounded from
the upper side by the same expression of the efficiency at maximum power:
$\eta_{mp}\leq\eta_+\equiv \eta_C^2/[\eta_C-(1-\eta_C)\ln(1-\eta_C)]$, with
$\eta_C=1-T_c/T_h$ the Carnot efficiency, which displays the same universality
of the CA efficiency $\eta_{CA}=1-\sqrt{1-\eta_C}$ at small relative
temperature difference. Within context of irreversible thermodynamics, we
calculate the Onsager coefficients and, we show that the value of $\eta_{CA}$
is indeed the upper bound of EMP for the Otto engines working in the
linear-response regime.
