  We present an experimentally feasible and efficient method for detecting
entangled states with measurements that extend naturally to a tomographically
complete set. Our detection criterion is based on measurements from subsets of
a quantum 2-design, e.g., mutually unbiased bases or symmetric informationally
complete states, and has several advantages over standard entanglement
witnesses. First, as more detectors in the measurement are applied, there is a
higher chance of witnessing a larger set of entangled states, in such a way
that the measurement setting converges to a complete setup for quantum state
tomography. Secondly, our method is twice as effective as standard witnesses in
the sense that both upper and lower bounds can be derived. Thirdly, the scheme
can be readily applied to measurement-device-independent scenarios.
