  Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC)
positive operator-valued measurements (POVMs) are two related topics in quantum
information theory. They are generalized to mutually unbiased measurements
(MUMs) and general symmetric informationally complete (GSIC) measurements,
respectively, that are both not necessarily rank 1. We study the quantum
separability problem by using these measurements and present separability
criteria for bipartite systems with arbitrary dimensions and multipartite
systems of multi-level subsystems. These criteria are proved to be more
effective than previous criteria especially when the dimensions of the
subsystems are different. Furthermore, full quantum state tomography is not
needed when these criteria are implemented in experiment.
