  We investigate whether paradigmatic measurements for quantum state
tomography, namely mutually unbiased bases and symmetric informationally
complete measurements, can be employed to certify quantum correlations. For
this purpose, we identify a simple and noise-robust correlation witness for
entanglement detection, steering and nonlocality that can be evaluated based on
the outcome statistics obtained in the tomography experiment. This allows us to
perform state tomography on entangled qutrits, a test of
Einstein-Podolsky-Rosen steering and a Bell inequality test, all within a
single experiment. We also investigate the trade-off between quantum
correlations and subsets of tomographically complete measurements as well as
the quantification of entanglement in the different scenarios. Finally, we
perform a photonics experiment in which we demonstrate quantum correlations
under these flexible assumptions, namely with both parties trusted, one party
untrusted and both parties untrusted.
