  The dynamics of quantum discord is studied in a system of two identical
noninteracting qubits coupled to a common squeezed vacuum bath through
non-demolition interactions. We concern on how reservoir squeezing influences
the dynamical behaviors of quantum discord when both qubits are initially
prepared in $X$-type states. We find that the critical time exhibits the sudden
change of quantum discord, which is of great significance for the quantum
discord amplification. Furthermore, depending on the initial parameters of the
system, we numerically calculate the interval when the critical time is finite
or infinite. For the finite critical time, we show that the squeezing phase of
the bath can prolong the critical time while the squeezing strength exhibits
the opposite effect. For infinite critical time, even if there is no sudden
transition point, reservoir squeezing still has an effect on the amplification
of quantum discord, and the time to reach steady-state quantum discord can be
changed by adjusting the squeezing parameters. Fianlly, we investigate the
quantum speed limit time for a two-qubit system under squeezed reservoir, and
find that the quantum speed limit time can be reduced via the adjustment of the
squeezing parameters and the initial parameters. Remarkably, in the short time
limit, reservoir squeezing has an obvious influence on the degree of
amplification of quantum discord. Our study presents a promising approach to
controlling the amplification of quantum correlation.
