Kuznetsov component A_X of an algebraic variety X is defined to be the right orthogonal of some exceptional collection in the bounded derived category of X. When X is a cubic fourfold or Gushel Mukai fourfold, A_X is a noncommutative K3 surface in the sense that its Serre functor is given by "shifting by 2". Whether or not A_X is equivalent to the bounded derived category of an actual K3 surface is believed to be related to the rationality of the variety X , therefore it has received extensive studies. Yet not many studies seem to answer the question of when the Kuznetsov component of a cubic fourfold is equivalent to that of a Gushel Mukai fourfold, we believe that the answer of this question should be interesting for it will give a part of "Torelli theorem for noncommutative K3 surfaces". In this talk, I will present some partial results which address the previous question.