  The small-scale linear information in galaxy samples typically lost during
non-linear growth can be restored to a certain level by the density field
reconstruction, which has been demonstrated for improving the precision of the
baryon acoustic oscillations (BAO) measurements. As proposed in the literature,
a joint analysis of the power spectrum before and after the reconstruction
enables an efficient extraction of information carried by high-order
statistics. However, the statistics of the post-reconstruction density field
are difficult to model. In this work, we circumvent this issue by developing an
accurate emulator for the pre-reconstructed, post-reconstructed, and cross
power spectra ($P_{\rm pre}$, $P_{\rm post}$, $P_{\rm cross}$) up to
$k=0.5~h~{\rm Mpc^{-1}}$ based on the \textsc{Dark Quest} N-body simulations.
The accuracy of the emulator is at percent level, namely, the error of the
emulated monopole and quadrupole of the power spectra is less than $1\%$ and
$10\%$ of the ground truth, respectively. A fit to an example power spectra
using the emulator shows that the constraints on cosmological parameters get
largely improved using $P_{\rm pre}$+$P_{\rm post}$+$P_{\rm cross}$ with
$k_{\rm max}=0.25~h~{\rm Mpc^{-1}}$, compared to that derived from $P_{\rm
pre}$ alone, namely, the constraints on ($\Omega_m$, $H_0$, $\sigma_8$) are
tightened by $\sim41 \%-55\%$, and the uncertainties of the derived BAO and RSD
parameters ($\alpha_{\perp}$, $\alpha_{||}$, $f\sigma_8$) shrink by $\sim
28\%-54\%$, respectively. This highlights the complementarity among $P_{\rm
pre}$, $P_{\rm post}$ and $P_{\rm cross}$, which demonstrates the efficiency
and practicability of a joint $P_{\rm pre}$, $P_{\rm post}$ and $P_{\rm cross}$
analysis for cosmological implications.
