No, that's not true. If it were then there could never be direct observation of quantum interference because entangled particles do not self-interfere.
It is true that entanglement is very common, and an unentangled state is the unusual case. But it's not true that unentangled states (or, to be precise, unentangled degrees of freedom) don't exist.
> because entangled particles do not self-interfere
Entangled particles certainly can, and do interfere (as mentioned, electrons in an atom are entangled and definitely interfere; there's a whole field devoted to calculating this effect), so I'm not sure exactly what you mean here. Can you give me, in ket notation, an example of an unentangled state? (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.
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?
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.
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.
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.
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.)
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.)
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?)
Oh certainly. I've never disagreed on this haha.
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.