Talk:Quantum correlation

This article misses the point about quantum correlation. The historical context first: When von Neumann attempted to prove the non-existence of hidden variables, he referred to variances and various properties of observables assuming that they made sense generally even for non-commuting observables. You make no reference to this at all nor to the relation of correlation to measurement which is an essential point in understanding why von Neumann's proof was wrong.

Moreover you only refer to quantum correlation for a Bell test setup. This needs to be handled for much more general pairs of observables.CSTAR 23:05, 24 Jan 2005 (UTC)

Agreed. This article, as currently written, contains no usable information. If I had some observables in my pocket, I would have no clue if the quantities I'm computing are called quantum correlations or not. I don't like the fact that none of my textbooks on QM even appear to use this term. Part of me says "VfD the thing". linas 13:55, 25 July 2005 (UTC)[reply]

Let me restate that. When QM is taught, one of the earlier lessons is how to compute expectation values of observables, and how to make experimental measurements of observables. This will include examples where the observables being measured don't commute with the observables with which the state is prepared. Concepts such as coincidence counts will be discussed; that's because there are a variety of two-particle effects that have nothing to do with Bell's thm. Throughout all of this presentation, the words "quantum correlation" will never be used. That's because, in this context, the word "correlation" has exactly the same meaning as it does for the probability and statistics guys.

This article seems to imply that there is some sort of other "correlation" that is special, and applies only to quantum mechanics. It seems to imply that "quantum correlation" is somehow different than the "classical correlation" that probability and statistics types talk about. But, as a concept, there is no such thing as quantum correlation. This phrase exists only as a concatenation of the adjective "quantum" to the noun "correlation" and this phrase is handy when discussing certain types of inequalities. However, it is not a concept with any sort of independent existence. As such, it doesn't warrent an encyclopedia article; except maybe an article that states "there is no such thing". linas 14:22, 25 July 2005 (UTC)[reply]

Hmmm ... you could be right. Though searching Google or the quant-ph archive reveals many occurrences of the phrase "quantum correlation", the term is not necessarily always being used in Bell's manner. There is quite a strong tradition in papers concerned with entanglement of assuming Bell's definition, i.e.

QC(a, b) = ∫ dλ ρ(λ) A(a, λ)B(b, λ)

where A and B are possible "outcomes" on each side of a Bell test experiment. [Based on equation (2) of Bell's "On the Einstein-Podolsky-Rosen paradox"]

Caroline Thompson 21:16, 25 July 2005 (UTC)[reply]

I revised this page late last night and am not sure I've got it right. I found myself inevitably beginning to transform it into a page on the detection loophole. The point is that the local realist formula can cover null outcomes easily, but the QM one (which I probably should have given as well) is only intended for the case where all outcomes are +1 or -1. The only way of making the QM theory apply to experiments with inefficient detectors is to assume that we can take just the set of coincidences and treat these as if they were the set of emitted pairs. In other words, we are forced to assume "fair sampling". This is why the separate definition of "quantum correlation" is important. When there are no null results, because the mean on each side is (under rotational invariance) zero and because all results have absolute value 1, the definition coincides with the ordinary one. When there are some null values, the difference become critical. [This para is copied from the "Bell's theorem" talk page.] Caroline Thompson 08:30, 26 July 2005 (UTC)[reply]

This seems to be turning into another article on the Bell test; it now says even less about "quantum correlations" than it used to. I don't like this new twist very much at all. It would be better to merge this into the article on Bell tests. linas 14:04, 28 July 2005 (UTC)[reply]

I agree with linas. This article says absolutely nothing about the meaning of correlation of any kind.--CSTAR 16:17, 28 July 2005 (UTC)[reply]

Surely it does say something! There is no intention of saying what a correlation is -- that is taken as known. What the page is intended to do is say what quantum correlation (QC) means in the context of Bell tests. It says how to calculate it, then mentions the practical difficulty that arises when detectors are inefficient. It states the local realist prediction for QC. To complete it I need to add the QM prediction.

However, you are right: it is inevitably turning into a page on the detection loophole. The material here should be incorporated into a new page on the Bell test loopholes. I don't think it belongs in Bell test experiments since it is a theoretical matter that would distract from the main theme and make the page too long. Also, it is the kind of info that ought to be referred to from several other pages.

Unless, of course, the coverage of the matter in Bell's theorem is improved! As it stands, there is no way the reader is going to grasp what the fuss about the detection loophole is all about. It is really quite simple: the derivations of the Bell inequalities all assume we are talking about QC as I define it, and it is taken for granted that a fair estimate will be used. This fair estimate it obviously the ordinary average of the product of outcomes, so that the divisor is necessarily the number of pairs that were emitted. The use of the "accepted" divisor (the sum of observed coincidences) has never, to my knowledge, been supported by any theoretical arguments. It has always been just a matter of belief: the sample of detected pairs has no reason (quantum theorists think) not to be a fair one. To a local realist, this belief is ludicrous! See my own work or even that of some members of the establishment, e.g. Gisin and Gisin's 1999 paper. Caroline Thompson 08:51, 29 July 2005 (UTC)[reply]

There is no "quantum correlation" but Quantum correlations.

I think this article misses the point. Quantum Discord , Quantum work deficit on SEPARABLE states are also quantum correlations ... Not only Bell type violations are quantum ...

I agree with this. I think the article needs an improved structure. This reference (https://arxiv.org/abs/1501.03332) would definitely help into categorising quantum correlations (entanglement is a superset of EPR steerability, which is a superset of Bell nonlocality). Anyone willing to do it? Mcasariego (talk) 15:08, 17 September 2018 (UTC)[reply]