How does the interaction between two quantum systems form entanglement?

[alexepascual]

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.

 

[alexepascual]

Does anybody know the answer to this?

 

[DrChinese]

Does anybody know the answer to this?

I don't usually define this as entanglement. So that is why I didn't respond earlier. Is there a specific situation you are picturing?

 

[alexepascual]

I don't usually define this as entanglement. So that is why I didn't respond earlier. Is there a specific situation you are picturing?

Well, I can understand that you don't picture the measurement process as containing a phase where entanglement is formed. Probably you prefer to look at measurement as a projection of the system which does not involve the apparatus. But this is not my main concern here. I just would like to get a clearer picture of how entanglement happens.
So, considering two simple quantum systems that are initially not correlated, when they interact they get entangled. You are asking if I have a particular example in mind. I did give in my original post the example of two particles with spin 1/2 that are brought close to each other in such a way that their spins tend to point in opposite directions. I think there may be better examples but I like spin 1/2 because of the discrete Hilbert space.