  Time-local quantum master equations that describe open quantum systems beyond
the limit of ultraweak system-bath coupling are often not of
Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. Prominent examples are the
Redfield equation approximating general open quantum systems and the
Hu-Paz-Zhang equation exactly describing a damped harmonic oscillator. Here, we
show that not only the former, but also the latter can be brought to
pseudo-Lindblad form, with a dissipator that resembles that of a GKSL equation,
except for the fact that some of the terms have negative weights. Moreover, we
systematically investigate transformations that leave the dissipator of
pseudo-Lindblad equations unchanged, while changing the relative weight between
its positive and negative terms. These can be used to minimize the weights of
the negative terms, which is optimal both for the convergence of a recently
developed quantum-trajectory unraveling of pseudo-Lindblad equations as well as
for the truncation of the negative terms to obtain a GKSL equation.
