  We present a complete-quantum description of multi-particle Szilard engine
which consists of a working substance and a Maxwell's demon. The demon is
modeled as a multi-level quantum system with specific quantum control and the
working substance consists of identical particles obeying Bose-Einstein or
Fermi-Dirac statistics. In this description, a reversible scheme to erase the
demon's memory by a lower temperature heat bath is used. We demonstrate that
(1) the quantum control of the demon can be optimized for single-particle
Szilard engine so that the efficiency of the demon-assisted thermodynamic cycle
could reach the Carnot cycle's efficiency; (2) the low-temperature behavior of
the working substance is very sensitive to the quantum statistics of the
particles and the insertion position of the partition.
