Difference between interaction and interference of QM systems

[jdstokes]

Suppose I have n identical quantum mechanical systems $\mathcal{H}$ isolated from each other. It is a postulate of quantum mechanics that the states of this composite system are described by rays in the tensor product space $\mathcal{H}^{\otimes n}$.

If the states are not allowed to interfere with each other then the state will be a product state of the form $\otimes_{i=1}^n|\alpha_i \rangle$.

Interference between the wavefunctions opens the possibility of entangled states which cannot be factorized into the form above. In this case, the outcomes of measurements on each of the systems can affect the probabilities of the outcomes of measurements on the remaining systems. An example would be the $2^2$ dimensional Hilbert space associated with an electron/positron pair created in the decay of a neutral pion.

Is it correct to say that entanglement is a consequence of wavefunction intereference rather than interaction? In reality the electron/positron pair in the last exam interact via pairwise Coulomb interaction.

Can interactions other than wavefunction interference affect the entanglement between quantum mechanical systems?

 

[erastotenes]

If I am not wrong in all cases we know, entanglement(interference) is the result of a common (interacting) past as it is in your case.

So I would put the question this way: If two different pions decay at distant locations. Is it possible that the electron from the first decay can be entangled with the positron from the second decay?

I guess it is not principally impossible but it is extremely unlikely because coherence(interference) is an exceptional case (and can therefore occur only if there is a common past) where decoherence is the more general case.

Am I right?