> (And if you're referring to a direct tensor product of two single particle states, I'm still considering that an entangled state since it can unitarily evolve out of that configuration into one that can't be written as a tensor product)

This reasoning does not make sense. The notion of entanglement is not invariant under "global" operations, nor should it be.

> Quantum interference is observable with even a single particle.

Yes, but only if that particle is in an unentangled state. If that particle is entangled then the only way to observer the interference is to make measurements on both the particle whose interference you wish to observe and the particle with which it is entangled.

This is simply the old canard about measurement "destroying" interference (because measurement and entanglement are the same thing).

> Entangled particles certainly can, and do interfere

That's true, but the way in which they interfere is different, and the procedure you need to perform to observe the interference is likewise different.

> Can you give me, in ket notation, an example of an unentangled state?

|U> + |D>

Or if you want two unentangled particles:

(|U1> + |D1>)(|U2> + |D2>)

as opposed to the entangled state:

|U1>|D2> + |D1>|U2>

(Where U and D are intended to designate something like spin Up or spin Down, but that doesn't really matter.)

> if you're referring to a direct tensor product of two single particle states, I'm still considering that an entangled state since it can unitarily evolve out of that configuration into one that can't be written as a tensor product

That's news to me. How does that happen?

This debate has really been bothering me and making me anxious the last couple of days. I haven't been able to sleep. I need to know something, are you self-taught in quantum mechanics or do you have a PhD in theoretical physics?

I'm not doubting your argument, (for all I know you're a well-known physics professor), I would just really like an answer to this question, as I think it would put my mind at ease.

Self-taught. Why does that matter? (I do have a Ph.D. but it's in CS.)

P.S. It turns out you were right about this:

"it can unitarily evolve out of that configuration into one that can't be written as a tensor product"

That turns out to be true (and it retrospect it's obviously true because otherwise it would not be possible to create entangled pairs.) But you are wrong in your claim that therefore the antecedent state is also entangled. A state that can be factored is not entangled by definition.

> Self-taught. Why does that matter?

It doesn't. All that matters is that the science is correct (see Ron Maimon for instance; self-taught but far more knowledgable than most physicists). However, I get in far too many discussions involving QM online (mostly Reddit) where I learn that I wasted my time arguing with a 14 year old that watched "Through the wormhole" or something.

> P.S. It turns out you were right about this

You sound surprised. My graduate research is in quantum chemistry (and related areas), so I should have at least a few concepts correct. As someone with more of a QC background, perhaps my definition of what theoretical physicists consider "entangled" is inaccurate, so I am reading up on the matter. But I'm finding their specification of "entangled" to be an unintuitive and unobvious choice of wording.

> I wasted my time arguing with a 14 year old

Well, I'm about to turn 50 so you don't have to worry about that. :-)

FWIW, I wrote this:

http://www.flownet.com/ron/QM.pdf

> You sound surprised.

No, I'm not. (How does one "sound surprised" in an on-line conversation?)

> perhaps my definition of what theoretical physicists consider "entangled" is inaccurate

An entangled state is one that can't be factored. See e.g.

http://www.theory.caltech.edu/people/preskill/ph229/notes/bo...

section 2.4.1.

(I am a bit nonplussed by how someone who does graduate research in quantum chemistry can not know this. It's a pretty basic concept.)

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.