  The difference between the $\Lambda$ and $\bar \Lambda$ longitudinal spin
transfers in the semi-inclusive deep inelastic scattering process is
intensively studied. The study is performed in the current fragmentation
region, by considering the intermediate hyperon decay processes and sea quark
fragmentation processes, while the strange sea $s\bar s$ asymmetry in the
nucleon is taken into account. The calculation in the light-cone quark-diquark
model shows that the strange sea asymmetry gives a proper trend to the
difference between the $\Lambda$ and $\bar \Lambda$ longitudinal spin
transfers. When considering the nonzero final hadron transverse momentum, our
results can explain the COMPASS data reasonably. The nonzero final hadron
transverse momentum is interpreted as a natural constraint to the final hadron
$z$ range where the longitudinal spin transfer is more sensitive to the strange
sea $s\bar s$ asymmetry.
