  Recently, a thermodynamic uncertainty relation (TUR) has been formulated for
classical Markovian systems demonstrating trade-off between precision (current
fluctuation) and cost (dissipation). Systems that violate the TUR are
interesting as they overcome another trade-off relation concerning the
efficiency of a heat engine, its power, and its stability (power fluctuations).
Here, we analyze the root, extent, and impact on performance of TUR violations
in quantum thermoelectric junctions at steady state. Considering noninteracting
electrons, first we show that only the "classical" component of the current
noise, arising from single-electron transfer events follows the TUR. The
remaining, "quantum" part of current noise is therefore responsible for the
potential violation of TUR in such quantum systems. Next, focusing on the
resonant transport regime we determine the parameter range in which the
violation of the TUR can be observed---for both voltage-biased junctions and
thermoelectric engines. We illustrate our findings with exact numerical
simulations of a serial double quantum dot system. Most significantly, we
demonstrate that the TUR always holds in noninteracting thermoelectric
generators when approaching the thermodynamic efficiency limit.
