the Si$_{3}$N$_{4}$ paddle nanocavity is expected to perform for phononic quantum non-demolition (QND) measurements [@Kaviani:15]. Although the $g^{(2)}$ for this device is almost two orders of magnitude lower than that of similar Si devices, the high internal stress of Si$_{3}$N$_{4}$ enables longer supports that in practice lower $\omega_m$. Stress engineering can be used to increase $Q_m$ and has resulted in record $Q_m \omega_m$ products in recently reported work [@ghadimi2018elastic; @tsaturyan2017ultracoherent]. This figure of merit is a measure of the ability of a mechanical resonator to maintain coherence in the presence of a thermal bath. Considering measurement shot noise and the expected change in cavity transmission due to a change in phonon number, as in Ref. [@Thompson2008], it is predicted that the signal-to-noise ratio $\Sigma^{(0)}$ = $\tau_{tot}^{(0)}\Delta\omega_{o}^{2}/S_{w_{o}}$ for a quantum jump measurement from the motional ground state to a single phonon Fock state could exceed unity for sufficiently high $Q_m$ and $L$, as shown in Fig. \[figureSix\](a). The $\Sigma^{(0)}$ for $Q_m$ = $10^2$, $10^5$ and $10^8$ (blue, orange and green curves respectively) is presented, assuming the device and its surroundings are cryogenically pre-cooled to a bath temperature $T_{b}~=~10$ mK, and that $Q_o$ = $10^6$. Here $\tau_{tot}^{(0)}~=~\hbar Q_m~/~k_{B}T_{b}$ (for Boltzmann’s constant $k_B$) 