  We study the quantum separability problem by using general symmetric
informationally complete measurements and present separability criteria for
both $d$-dimensional bipartite and multipartite systems. The criterion for
bipartite quantum states are effective in detecting several well known classes
of quantum states. For isotropic states, it becomes both necessary and
sufficient. Furthermore, our criteria can be experimentally implemented and the
criterion for two-qudit states requires less local measurements than the one
based on mutually unbiased measurements.
