  Space-time dependence of imaginary-time propagators, vital for \textit{ab
initio} and many-body calculations based on quantum field theories, has been
revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X
{\bf 13}, 021015 (2023)]. However, the impact of system parameters, like
temperature, on data size remains underexplored. This paper provides a
comprehensive numerical analysis of the compactness of local imaginary-time
propagators in QTT for one-time/-frequency objects and two-time/-frequency
objects, considering truncation in terms of the Frobenius and maximum norms. We
employ random pole models to study worst-case scenarios. The numerical analysis
reveals several key findings. For one-time/-frequency objects and
two-time/-frequency objects, the bond dimensions saturate at low temperatures,
especially for truncation in terms of the Frobenius norm. We provide
counting-number arguments for the saturation of bond dimensions for the
one-time/-frequency objects, while the origin of this saturation for
two-time/-frequency objects remains to be clarified. This paper's findings
highlight the critical need for further research on the selection of truncation
methods, tolerance levels, and the choice between imaginary-time and
imaginary-frequency representations in practical applications.
