  This paper justifies the compressible Euler and acoustic limits from quantum
Boltzmann equation with Fermi-Dirac statistics (briefly, BFD) rigorously. This
limit was formally derived in Zakrevskiy's thesis \cite{Zakrevskiy} by moment
method. We employ the Hilbert approach. The forms of the classical compressible
Euler system and the one derived from BFD are different. Our proof is based on
the analysis of the nonlinear implicit transformation of these two forms, and a
few novel nonlinear estimates.
