  Mutually unbiased bases, mutually unbiased measurements and general symmetric
informationally complete measurements are three related concepts in quantum
information theory. We investigate multipartite systems using these notions and
present some criteria detecting entanglement of arbitrary high dimensional
multi-qudit systems and multipartite systems of subsystems with different
dimensions. It is proved that these criteria can detect the $k$-nonseparability
($k$ is even) of multipartite qudit systems and arbitrary high dimensional
multipartite systems of $m$ subsystems with different dimensions. We show that
they are more efficient and wider of application range than the previous ones.
They provide experimental implementation in detecting entanglement without full
quantum state tomography.
