I understand the measurement process is sometimes divided into 1) a "premeasurement" which consists in the formation of correlations between system and apparatus (entanglement) and.. 2) a choice between the different eigenvectors of the observable's operator. I would like to understand better the first part of this process. Actually I just want to understand better the formation of entanglement, regardless of it being considered part of a measurement or not. Once I understand it better I can apply this new knowledge to my thinking about the measurement process. I have seen this formation of entanglement described as a unitary transformation. But I don't understand how that can be the case if the formation of correlations may imply the dissapearance of some combinations in the combined Hilbert space. For instance if we are bringing two spin 1/2 particles together which forces their spins point in opposite directions, then the previous situation before interaction which could include combinations where both particles spins point up would dissapear. This transformation would map vectors in a Hilbert space to vectors in anothe Hilbert space of lower dimensionality. Can this be a unitary transformation? (It seems to me this should be a matrix with determinant = 0, not 1) If anybody can point me to some book or article which clariffies this issue I would also appreciate it.