  Young massive stars are usually found embedded in dense massive molecular
clumps and are known for being highly obscured and distant. During their
formation process, deuteration is regarded as a potentially good indicator of
the very early formation stages. In this work, we test the observability of the
ground-state transition of ortho-H$_2$D$^+$ $J_{\rm {K_a, K_c}} =
1_{10}$-$1_{11} $ by performing interferometric and single-dish synthetic
observations using magneto-hydrodynamic simulations of high-mass collapsing
molecular cores, including deuteration chemistry. We studied different
evolutionary times and source distances (from 1 to 7 kpc) to estimate the
information loss when comparing the column densities inferred from the
synthetic observations to the column densities in the model. We mimicked
single-dish observations considering an APEX-like beam and interferometric
observations using CASA and assuming the most compact configuration for the
ALMA antennas. We found that, for centrally concentrated density distributions,
the column densities are underestimated by about 51% in the case of
high-resolution ALMA observations ($\leqslant$1") and up to 90% for APEX
observations (17"). Interferometers retrieve values closer to the real ones,
however, their finite spatial sampling results in the loss of contribution from
large-scale structures due to the lack of short baselines. We conclude that,
the emission of o-H$_2$D$^+$ in distant massive dense cores is faint and would
require from $\sim$1 to $\sim$7 hours of observation at distances of 1 and 7
kpc, respectively, to achieve a 14$\sigma$ detection in the best case scenario.
Additionally, the column densities derived from such observations will
certainly be affected by beam dilution in the case of single-dishes and spatial
filtering in the case of interferometers.
