  The thermodynamic uncertainty relations (TURs), originally discovered for
classical systems, dictate the trade-off between dissipation and fluctuations
of irreversible current, specifying a minimal bound that constrains the two
quantities. In a series of effort to extend the relation to the one under more
generalized conditions, it has been noticed that the bound is less tight in
open quantum processes. To study the origin of the loose bounds, we consider an
external field-driven transition dynamics of two-level quantum system weakly
coupled to the bosonic bath as a model of open quantum system. The model makes
it explicit that the imaginary part of quantum coherence, which contributes to
dissipation to the environment, is responsible for loosening the TUR bound by
suppressing the relative fluctuations in the irreversible current of
transitions, whereas the real part of the coherence tightens it. Our study
offers a better understanding of how quantum nature affects the TUR bound.
