A foundational question about entanglement

Question

The recent Nature article http://www.nature.com/news/data-teleportation-the-quantum-space-race-1.11958 prompts me to ask this question, which is of the same tenor as that asked at the recent Perimeter Institute meeting attended by Zeilinger et al., i.e. "Do the pairs somehow communicate though some still-unknown information channel?"

It seems to me that entanglement could be described as behaving as if in some sense the coordinate separation is described by an extra degree of freedom (dimension) in which either a) the two entangled components are co-located in the extra dimension, allowing instantaneous communication; or b) in the extra dimension, the speed of light is no longer a limitation, and so co-location is not a requirement. ... or some mixture of the two. This could all be rephrased in terms of the concepts of "brane" and "bulk", of course.

Are there many other such "unconventional" interpretations of the nature of entanglement out there?

Answer 1

Do the pairs somehow communicate though some still-unknown information channel? No.

Entanglement is, in essence, a quantum correlation and correlations do not imply/require the transmission of any information between the correlated elements. Since there is no transmission of anything, there is no need to invoke or invent a mechanism neither superluminal nor of any other nature.

One of Zeilinger traditional mistakes is that he treats the correlated pair as if was non-correlated and then he is forced to introduce what he calls "the spooky effect at a distance" mechanism for explaining the synch observed in the experimental data.

A rather good discussion of all those topics is given in the textbook by Griffiths "Consistent Quantum Theory" (Cambridge University Press):

The idea that the quantum world is permeated by superluminal influences has come about because of an inadequate understanding of quantum measurements [...] or through assuming the existence of hidden variables instead of (or in addition to) the quantum Hilbert space [...] By contrast, a consistent application of quantum principles provides a positive demonstration of the absence of nonlocal influences, as in the example discussed in Sec. 23.4.

Answer 2

entanglement is only manifest because entangled components usually have a well-defined total quantum number (like angular momentum) but no defined quantum number of its parts. Locally, quantum mechanics will make both parts to have a dispersive amplitude over different eigenvalues, but global conservation of the quantum number will guarantee that only remote observers eigenstates that have individual quantum numbers such that the global number is conserved will be able to interact to each other.

Answer 3

I'm gonna paste this from https://golem.ph.utexas.edu/~distler/blog/archives/003186.html as a complement to juanrga's answer that entanglement is a mere correlation:

“Entanglement” is a bit tricky to explain, versus “correlation” — which has a perfectly classical interpretation.

Say I tear a page of paper in two, crumple up the two pieces into balls and (at random) hand one to Adam and the other to Betty. They then go their separate ways and — sometime later — Adam unfolds his piece of paper. There’s a 50% chance that he got the top half, and 50% that he got the bottom half. But if he got the top half, we know for certain that Betty got the bottom half (and vice versa).

That’s correlation.

In this regard, the entangled state behaves exactly the same way. What distinguishes the entangled state from the merely correlated is something that doesn’t have a classical analogue. So let me shift from pieces of paper to photons.

You’re probably familiar with the polaroid filters in good sunglasses. They absorb light polarized along the horizontal axis, but transmit light polarized along the vertical axis.

Say, instead of crumpled pieces of paper, I send Adam and Betty a pair of photons.

In the correlated state, one photon is polarized horizontally, and one photon is polarized vertically, and there’s a 50% chance that Adam got the first while Betty got the second and a 50% chance that it’s the other way around.

Adam and Betty send their photons through polaroid filters, both aligned vertically. If Adam’s photon makes it through the filter, we can be certain that Betty’s gets absorbed and vice versa. Same is true if they both align their filters horizontally.

Say Adam aligns his filter horizontally, while Betty aligns hers vertically. Then either both photons make it though (with 50% probability) or both get absorbed (also with 50% probability).

All of the above statements are also true in the entangled state.

The tricky thing, the thing that makes the entangled state different from the correlated state, is what happens if both Adam and Betty align their filters at a 45° angle. Now there’s a 50% chance that Adam’s photon makes it through his filter, and a 50% chance that Betty’s photon makes it through her filter.

(You can check this yourself, if you’re willing to sacrifice an old pair of sunglasses. Polarize a beam of light with one sunglass lens, and view it through the other sunglass lens. As you rotate the second lens, the intensity varies from 100% (when the lenses are aligned) to 0 (when they are at 90°). The intensity is 50% when the second lens is at 45°.)

So what is the probability that both Adam and Betty’s photons make it through? Well, if there’s a 50% chance that his made it through and a 50% chance that hers made it through, then you might surmise that there’s a 25% chance that both made it through.

That’s indeed the correct answer in the correlated state.

In fact, in the correlated state, each of the 4 possible outcomes (both photons made it through, Adam’s made it through but Betty’s got absorbed, Adam’s got absorbed but Betty’s made it through or both got absorbed) has a 25% chance of taking place.

But, in the entangled state, things are different.

In the entangled state, the probability that both photons made it through is 50% – the same as the probability that one made it through. In other words, if Adam’s photon made it through the 45° filter, then we can be certain that Betty’s made it through. And if Adam’s was absorbed, so was Betty’s. There’s zero chance that one of their photons made it through while the other got absorbed.

Unfortunately, while it’s fairly easy to create the correlated state with classical tools (polaroid filters, half-silvered mirrors, …), creating the entangled state requires some quantum mechanical ingredients. So you’ll just have to believe me that quantum mechanics allows for a state of two photons with all of the aforementioned properties.

Sorry if this explanation was a bit convoluted; I told you that entanglement is subtle…

Getting back to the answer, it needs to be noted that in the Copenhagen interpretation of quantum mechanics, the paradox persists and instantaneous influences are indeed required to explain the phenomena.

But there is indeed a class of interpretations (Consistent Histories, Many Worlds, etc.) in which the paradox is claimed to be non-existent.