  Nanoscale heat engines are subject to large fluctuations which affect their
precision. The Thermodynamic Uncertainty Relation (TUR) provides a trade-off
between output power, fluctuations and entropic cost. This trade-off may be
overcome by systems exhibiting quantum coherence. This letter provides a study
of the TUR in a prototypical quantum heat engine, the Scovil & Schulz-DuBois
maser. Comparison with a classical reference system allows us to determine the
effect of quantum coherence on the performance of the heat engine. We identify
analytically regions where coherence suppresses fluctuations, implying a
quantum advantage, as well as regions where fluctuations are enhanced by
coherence. This quantum effect cannot be anticipated from the off-diagonal
elements of the density matrix. Because the fluctuations are not encoded in the
steady state alone, TUR violations are a consequence of coherence that goes
beyond steady-state coherence. While the system violates the conventional TUR,
it adheres a recent formulation of a quantum TUR. We further show that
parameters where the engine operates close to the conventional limit are
prevalent and TUR violations in the quantum model not uncommon.

Quantum Physics