There are other approaches for tomography that need fewer measurements than full quantum state tomography. As we have discussed, PI tomography is typically most useful for quantum states that are close to being permutionally invariant. Compressed sensing is especially suited for low rank states. Matrix product state tomography is most suitable for, e.g., cluster states and ground states of spin models. Permutationally invariant tomography can be combined with compressed sensing. In this case, the number of local measurement settings needed can even be smaller than for permutationally invariant tomography.