  We introduce $\Lambda$-moments with respect to any positive map $\Lambda$. We
show that these $\Lambda$-moments can effectively characterize the entanglement
of unknown quantum states without theirs prior reconstructions. Based on
$\Lambda$-moments necessary and sufficient separability criteria, as well as
necessary optimized criteria are presented, which include the ones in
[\href{https://link.aps.org/doi/10.1103/PhysRevLett.127.060504}{Phys. Rev.
Lett. \textbf{127}, 060504 (2021)}] as special cases. Detailed example is given
to show that our criteria can detect bound entanglement that can not be
identified by positive partial transpose criterion, with the explicit
measurement operators to experimentally measure the corresponding
$\Lambda$-moments.
