a similar definition is used for $\check{p}$. Initially, with feedforward turned off ($w = 0$ for $t < t^*$), the upconverted signal, a $2\pi \times 5~\mathrm{Hz}$ quadrature oscillation, is difficult to resolve (Fig. \[feedforward\]a). After feedforward is turned on ($w = 1.6$ for $t > t^*$), the weak signal becomes clearly visible. To quantify the improvement, the optical quadratures $(\check{q}_\mathrm{o}, \check{p}_\mathrm{o})$ are repeatedly measured without a signal tone, as shown in Fig. \[feedforward\]b. The quadratures are Gaussian distributed (Fig. \[feedforward\]c), and feedforward reduces each quadrature variance by $59\%$.

Feedforward performance is limited mainly by the addition of uncorrelated noise from imperfect measurement chains. This limitation can be understood by examining the power spectral density of the feedforward signal, $\langle\check{X}^2_\mathrm{o}\rangle+\langle\check{Y}^2_\mathrm{o}\rangle$, where $$\begin{aligned}
\langle \check{X}^2_\mathrm{o} \rangle &=& \langle X_\mathrm{o}^2 \rangle + w^2 \frac{n_\mathrm{o}}{n_\mathrm{e}} \langle X_\mathrm{e}^2 \rangle - 2 w \sqrt{\frac{n_\mathrm{o}}{n_\mathrm{e}}} \langle X_\mathrm{e} X_\mathrm{o} \rangle, \\
\langle \check{Y}^2_\mathrm{o} \rangle  &=& \langle Y_\mathrm{o}^2 \rangle + w^2 \frac{n_\mathrm{o}}{n_\mathrm{e}} \langle Y_\mathrm{e}^2 \rangle - 2 w \sqrt{\frac{n_\mathrm{o}}{n_\mathrm{e}}} \langle Y_\mathrm{e} Y_\mathrm{o} \rangle,\end{aligned}$$ in terms of the measured real and imaginary spectral densities. As shown in Fig. \[feedforward\]d, as the feedforward weight $w$ is increased, the peak noise power near $f_\mathrm{m}$ decreases due to the presence of correlations near 