  For finite-time quantum Otto heat engine with working fluid consisting of
either a (i) qubit or (ii) a harmonic oscillator, we show that the relative
fluctuation of output work is always greater than the corresponding relative
fluctuation of input heat absorbed from the hot bath. As a result, the ratio
between the work fluctuation and the input heat fluctuation receives a lower
bound in terms of the square value of the average efficiency of the engine. The
saturation of the lower bound is received in the quasi-static limit of the
engine and can be shown for a class of working fluids that follow a
scale-invariant energy eigenspectra under driving.
