You really shouldn't be nonplussed about it (which, I'm not sure if you intended it this way, but calling it a "basic" concept seems a little passive aggressive. I could equally say that someone self-taught in QM should know the "basic" fact that product states would unitarily evolve out of that configuration). It just depends on what area you focus on and what your background is. Scott Aaronson says on his blog that he has explained Bell's Theorem to QFT professors that had never heard of it. Just wasn't relevant to their work. Does that make them bad physicists for not knowing such a well-known part of QM?

Heck, it's better than a professor I had that did DFT work who thought the single-particle wavefunction was the most fundamental aspect of quantum mechanics. Nevermind the fact that DFT is trashed for its lack of ability to account for electron correlation.

(And I do mean trashed. I was at the Gordon Research Conference in quantum chemistry this past summer where Peter Gill gave a lecture titled "the obituary of DFT". And if anyone has a right to rag on it, it's certainly him.)

> I could equally say that someone self-taught in QM should know the "basic" fact that product states would unitarily evolve out of that configuration.

Well, that would depend on how far my studies have gotten me, no? My general assumption is that anyone who actually does QM for a living knows at least as much as I do, and almost certainly a great deal more. (Case in point: I presume that QFT is quantum field theory, but what is DFT?) I prefer to view this as humility rather than passive aggression. In any case, I don't think either one of us should be losing any sleep over it :-)

But can we agree that there are states that can be factored, and states that can't, and that this is a useful distinction to make? And that this distinction is physical, i.e. that it produces observable effects? (And not just observable, but interesting and useful?)

> But can we agree that there are states that can be factored, and states that can't, and that this is a useful distinction to make? And that this distinction is physical, i.e. that it produces observable effects? (And not just observable, but interesting and useful?)

Oh certainly. I've never disagreed on this haha.

If you say so. "All components of a quantum system are always entangled" sounds like a contrary claim to me, but I don't want to quibble over it.

It does make an interesting puzzle, though, how it can be physically possible to prepare a state that is both unentangled and pure. I don't actually know the answer to that off the top of my head.