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A couple of questions:

1. Why should there necessarily be only the one hidden variable λ? In a paper I've just glanced through (Greenberger, Daniel M, “Two-particle versus three-particle EPR experiments”, Annals of the New York Academy of Sciences 755, 585-599 (1995)) they allow for three hidden variables, though (for some reason I have not yet fathomed) restricted so that the sum is zero.

2. Has the QM prediction been experimentally verified?

Caroline Thompson 18:02, 20 Aug 2004 (UTC)

Actual experiments[edit]

This experiment has taken place (at least once!). Here is one: http://arxiv.org/abs/quant-ph/9810035

Here is a local hidden variable theory that creeps in through error in a real experiment (where the simultaneous eigenstate cannot be obtained, only an approximate eigenstate obtained) http://arxiv.org/pdf/quant-ph/0007102

And here is an analysis of the results of the experiment, that claims to eliminate the possibility of a LHVT explaining the results of that experiment http://arxiv.org/pdf/quant-ph/9811013

In addition I have my five pennies:

Now let us suppose there are LHVs situated in the respective measuring devices. Let us denote them with: Sa for A, Sb for B and Sc for C. As an example we may take Sa to be an array of +1/-1 that are out of control of the experimenter (here in the example below A related Alice).

We have

Sa=(-1,+1,+1,-1, ... ,-1, ... ,-1 ...)

in an N-dimensional space: {-1,1}x{{-1,1}x...x{-1,1}x.... (x cartesian product here).

Furthermore, let us suppose that Alice, Bob and Claudia cannot change the setting of their measuring device without disturbing in an uncontrollable manner the Sa, Sb, and, Sc. This would lead to a different set of equations 1 ...4. We see:

1. A( a2 , λ, Sa ) B( b2 , λ, Sb ) C( c2 , λ, Sc ) = -1, 2. A( a2 , λ, Sa ) B( b1 , λ, Sb' ) C( c1 , λ, Sc' ) = 1, 3. A( a1 , λ, Sa' ) B( b2 , λ, Sb ) C( c1 , λ, Sc' ) = 1, and 4. A( a1 , λ ,Sa') B( b1 , λ, Sb' ) C( c2 , λ,Sc ) = 1.

That is, if, e.g., A changes the parameter setting from a2 to a1, the hidden state denoted with Sa will transform from its original state to an unkown state Sa' that cannot be controlled by the experimenter (here Alice). For instance, if we start from

Sa=(-1,+1,+1,-1, ... ,-1, ... ,-1 ...),

after the change of a2 to a1, we could see (e.g.)

Sa'=(+1,+1,+1,+1, ... ,-1, ... ,+1 ...)

and note that when a1 is changed back to a2, Sa, can arise that most likely is different from Sa.

If this scheme of uncontrollable changes in spin-like local (namely hidden in the measurement apparatus) variables, then GHZ will not reach a contradiction. In fact, I would like to ask GHZ how they plan to have for Alice, Bob and Claudia exactly the same value for the local hiden variables in order to arrive at the contradiction. What should the experimenters do to get that?

Yours Han Geurdes —Preceding unsigned comment added by (talk) 13:32, 19 February 2009 (UTC)[reply]

Actual Experiments II[edit]

The first source you mentioned is only talking about three-photon entanglement. Though some of the authors did a GHZ-experiment ("Experimental Test of Quantum Nonlocality in Three-photon GHZ Entanglement", Nature 403, 515 (2000)), accessible via D. Bouwmeester's website

It would be very nice to add some information about the real experiments. --QBenni (talk) 17:11, 17 January 2011 (UTC)[reply]

Treatment too technical?[edit]

Since physics scholars probably look elsewhere anyway, I think this article (and some of its relatives) should cater, at least in their introduction, to a lower level of expertise. I don't consider myself awfully ignorant yet I certainly have trouble following it.

The GHZ experiment, if I understand correctly, starts with two entangled pairs and then does an obliviating operation on one of the four photons to create 3 partially entangled photons. This seems interesting but the article doesn't even mention it (unless it's hidden among the math in a way that's indecipherable to me). I'm curious how the obliviating operation on the 4th photon is performed; not only doesn't this article tell me, it offers no clear external ref for this. I did fashion a Google search string that directed me to many appropriate-looking on-line papers (Happy face) ... but essentially every one of these was of the "pay per view" type. (Sad face)

Just my 2-cents' worth. Jamesdowallen (talk) 12:45, 20 October 2009 (UTC)[reply]

I've done my best to make this article more understandable by adding a few explanatory sentences to the intro, and adding a less-technical summary section. An explanation of the obliviating process remains to be done.
J-Wiki (talk) 00:36, 18 April 2011 (UTC)[reply]

+45° from horizontal, +45° from vertical[edit]

Without orientation, 45° from horizontal and vertical is the same. Does that sentence ("...+45° from horizontal. However, quantum mechanical theory predicts that it will be +45° from vertical...") mean that the predictions differ by 90°? It would be helpful to say so explicitly. --User:Haraldmmueller 19:19, 30 April 2018 (UTC)[reply]

In the language of quantum computation[edit]

I am thinking that this article may benefit from mentioning a description of the experiment in a language familiar to people who study quantum computation (i.e. the language of qubits, Pauli measurements, etc.).

In short, the state is , and the paradoxical measurements are Pauli , , , and measurements, which will always give results +1, -1, -1, and -1 respectively, contrary to how a local hidden-variable theory would predict to be possible.

In more technical language, is stabilized by , , , and . Those Pauli operators commute with each other, and their product is , despite there being 3 minus signs in the front, and 2 instances of and 2 of at each position. This is because , despite ; the GHZ experiment is just a clever way to demonstrate this with only overall commuting observables.

Reference: Experimental test of the Greenberger–Horne–Zeilinger-type paradoxes in and beyond graph states. Bbbbbbbbba (talk) 03:09, 29 March 2024 (UTC)[reply]

In fact, when I carefully read the current "Detailed technical example" section, I think it is less really detailed and more just obtuse. Apparently most of the notations was copied from GHZ's original paper ("Bell's theorem without inequalities"), which as is often the case for the founding paper on a topic, isn't the easiest to understand. Does anyone else agree that maybe we should just remove this section altogether and replace it with a "modern" description? Bbbbbbbbba (talk) 15:52, 29 March 2024 (UTC)[reply]
I added a section myself, and in the process noticed that there seems to be no satisfactory introduction to the multi-qubit Pauli algebra on Wikipedia (if anyone knows or writes such an introduction, please link to it!). For what it's worth, it may be easier for a layman to understand the quantum prediction if we expand the GHZ state in those Pauli bases, e.g.
But on the other hand, that would be even more mathematical formulas on the page, and would be quite cumbersome to verify, so I'm not sure if that would be worth it. Bbbbbbbbba (talk) 09:05, 30 March 2024 (UTC)[reply]
Yeah we do not have a Wikiproject for Quantum Computing and most of these subjects are lacking proper modern treatment. If you have a series of ideas of implement leave a message at WT:PHYSICS.--ReyHahn (talk) 12:37, 31 March 2024 (UTC)[reply]