Talk:CHSH inequality

message: * Talk:CHSH inequality/Archive_1 (July 2004)
Hi,
May I suggest also to include criticism on the completeness of the CHSH. To be found at: link http://dx.doi.org/10.1016/j.rinp.2014.06.002.
If Alice and Bob are allowed additional random elements i.e. a four sided dice and an additional coin and a third person Carrol is allowed to randomly draw LHV models from a "model pool"(an urn with names of models for instance) then the CHSH contains a statistical loophole for LHV models violating S=E(1,1)-E(1,2)-E(2,1)-E(2,2), and Probability{|S| > 2 | using LHV} is nonzero for quartets (1,1),(1,2),(2,1) and (2,2).
Regards.  — Preceding unsigned comment added by Hgeurdes (talk • contribs) 10:14, 18 August 2014 (UTC)
replies: text: Although that is an interesting paper, a follow on article in the same journal argues that the above cited paper essentially relies on constructing a non-local hidden variable model. Such models are of course not necessarily ruled out by the CHSH inequality. See https://doi.org/10.1016/j.rinp.2015.06.002 . Randallbsmith (talk) 23:43, 23 February 2023 (UTC)
thread_title: Preceding Discussion

message: ----
Hello Franck
:I fear this problem with geometry is mainly a red herring.  It would help if you went back and re-read my Chaotic Ball model paper, this time forgetting all preconceptions.  The ball is assumed to move randomly about a fixed centre.  The assistants stand and look at it.  The directions of their gazes are the "detector settings" and are quite unambiguous.  This is only an analogy so accuracy does not matter.  If you look at something you will be facing a particular direction.  It is surely not beyond the wit of man to fix the two angles of gaze with respect to some fixed base line -- a wall of the room or something?
To take (some of) your points in turn:
[FW:] ... under which circumstances do you suppose "the system state" could undergo change, if not in general from one trial of the sequence to the next trial ?
:Yes, the state (the orientation of the ball) is assumed to change from one observation to the next, but randomly.  The "trial index" has no physical significance.  As I explained, in a real experiment one organises things to ensure that the source is always producing the same random set of states.  It makes sense to define one distribution function ρ(λ) to give the probability of emissions being in the state λ, and this probability distribution stays the same for all individual trials and all sub-experiments (groups of trials with the same fixed detector settings).
[CHT:] But what is it we are really trying to reach agreement on? The major issue, I thought, was whether or not the CHSH test as currently applied, using the sum of coincidence rates as denominator, is valid?
[FW:] I tried to address this already above: that's certainly valid, especially as being free of any particular assumptions which would have to be made in order to consider "non-detections".
:The CHSH inequality has only been proved true if the terms involved are all built from sums and differences of probabilities.  You are not going to be able to reliably get an unbiased estimate of a probability if you divide by the number of observed coincidences, since the observed coincidences are not the set you started with.  You have to divide by N, the number of emitted pairs.
[FW:] ... neither do they appear decisive about how to obtain the number "N", the "number of emissions" itself. 
: Read on and you will find that they realise that N is not in practice known and therefore recommend a different test, in fact the  CH74 one.  Later discussion by Bell of possible use of the CHSH inequality was always on the assumption that there would be an "event-ready" detector.  The number registered by this would be used as N.  No such experiment has even been done, though.  Even in pulsed laser experiments, where the number of pulses ought, one would have thought, to be known, this number does not seem to be used.
[FW:] ... it is at least one sensible approach, as well as the simplest, to define and count the "number of emissions", "N" as "number of detections" which is directly available. 
:My [chaotic ball model] is sufficient to illustrate the fact that the inequality if used with the number of detections as denominator cannot serve its original purpose.  Local realist models can infringe it if there are in fact some non-detections.  Clauser et al were aware of this.
[FW:] [Re the geometry of the ball model] ... Could you for starters please point out just where the "index" of a protractor would have to be placed, in the presumably "precise diagram" (fig. 2)? My above guess, "(on) the center C of the ball" may have been a misunderstanding, of course. (I also note that the "Vectors a and b" of fig. 2 have no intersection drawn at all ...) 
: As explained above, there is absolutely no problem here.  And just why you think angles have to be defined in terms of distances I have no idea.  Can't you talk about the direction of the sun without any reference to distance?
[CHT:] But perhaps more importantly, if you think you can estimate the angle from the observed counts (assuming Malus' Law) this is entirely begging the issue!
[FW:] it certainly underscores the importance of CHSH's suggestions as thought experiments ...
: The CHSH 1969 paper is not about thought experiment but real ones.  The results of the first real one using ideas from the paper (though not the "CHSH test" but the CH74 single-channel one) were published in 1972.
[CHT:] I have seen the formula you use ("ArcCos[ (NN + SS - NS - SN) / (NN + SS + NS + SN) ]") elsewhere, but that does not make it meaningful.
[FW:] The fact that this formula represents a mathematically unambiguous expression in terms of actual experimental counts (based on your own definition) does make it meaningful; a physical quantity to be measured ...
:OK
[FW:] Since the days of Malus, this quantity even has a name: the "orientation angle", e. g. between a pair of "polarizer axes" (or in the later version: between a pair of "analyzer axes"). 
: You're putting the cart before the horse, Franck!  Malus would never have dreamed to using the term "orientation angle" to mean anything other than the geometrical angle.
Yours, Caroline Thompson 09:22, 29 Jul 2004 (UTC)
thread_title: What CHSH really proved (and more on the Chaotic Ball geometry)

message: Dr Chinese, your wholesale elimination of refs to my Chaotic Ball paper and pruning out of links to the Bell test loopholes page has surely overstepped the mark! Can't we please be neutral, i.e. not biased towards the supposedly "accepted" POV?  It's not as if I was the only local realist in the world, or the only person to have realised the relevance of the fair sampling loophole to the validity of actual Bell test experiments.
As you will see, I've replaced the ref to my own paper by one to Gisin's.  Wikipedai is the worse for this, since my paper is considerably more comprehensible, giving an intuitive analogy that correctly covers the main logic of the fair sampling loophole. Caroline Thompson 21:45, 31 Jan 2005 (UTC)
replies: text: All other than Caroline: the substance of the debate on this is at talk:Bell's theorem, and is not duplicated on related articles.  Caroline: stop promoting yourself.  Your POV deserves the same relative attention as it would get in a QM textbook... so quit wasting our time with coy arguments about fair representation.  You have it with the Bell test loopholes article.--DrChinese 22:27, 31 Jan 2005 (UTC)
thread_title: Is wikipedia's policy of a "Neutral point of view" suppose to mean the blatant suppression of a minority one?

message: I just added this article to the list of inequalities, where, strangely, it did not appear earlier.  If anyone knows of others that should be there and are not, could they please add those too? Michael Hardy (talk) 14:13, 11 December 2008 (UTC)
thread_title:  List of inequalities 

message: Is it ok to remove the following paragraph from the article?  It doesn't seem to make sense - how can something be assumed to be a hidden variable *in an experiment*, rather than in a theory?
:"Note that in all actual Bell test experiments it is assumed that the source stays essentially constant, being characterised at any given instant by a state ("hidden variable") λ that has a constant distribution ρ(λ) and is unaffected by the choice of detector setting."
Nathaniel Virgo (talk) 15:42, 30 May 2011 (UTC)
replies: text: I agree. It's nonsense. The article generally is very poor. Experimental and theoretical issues are muddled and mixed. It's also very outdated in tone. The issues discussed here were big things in the 70's but there has been enormous progress both in experiment and theory since then. Richard Gill (talk) 19:08, 5 June 2012 (UTC)
thread_title:  odd paragraph 

message: '...The constraint but can on the other hand be infringed by quantum mechanics....'
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The intended meaning of this sentence is elusive.
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I know 'butt-can' wasn't intended or any better, but it is the only thing that comes close to making sense.
70.185.109.98 (talk) 17:54, 4 February 2013 (UTC)
thread_title:  ..The constraint but can on the other hand be infringed.. 

message: I'm not clear from reading this. Should incidences be counted as +1, -1 or should they be counted as +1, 0?
103.118.46.247 (talk) 07:45, 3 November 2020 (UTC)
thread_title: The experimental estimate for <math>{\displaystyle E(a,b)}E(a, b)</math> is then calculated as: (see Eq. 3)

message: Please consider incorporating material from the above draft submission into this article. Drafts are eligible for deletion after 6 months of inactivity. ~Kvng (talk) 15:40, 5 August 2021 (UTC)
thread_title:  [[Draft:The CHSH Game]] 

message: I propose to merge CHSH game into CHSH inequality. I think that the content in the CHSH game article can easily be explained in the context of CHSH inequality, and the CHSH inequality article is of a reasonable size that the merging of CHSH game will not cause any problems as far as article size is concerned. Also both articles remain barely connected, a merge could improve their contents to make a more complete article. Another thing to consider is that CHSH game was a draft that was not accepted and was asked to be merged with CHSH inequality, but was published independently anyway.  ReyHahn (talk) 10:35, 5 September 2021 (UTC)
thread_title:  Merger proposal 

message: The article currently reads
> In the case of the 3 other possible input pairs, essentially identical analysis shows that Alice and Bob will have the same win probability
But this seems to be skipping over the most interesting part: If I understand correctly, as long as Alice still measures in the |0>, |1> basis the results are the same as if the initial qubit state was a hidden variable with a value of either 00 or 11. Only when the first measurement happens in a *different* basis the non-local entanglement of the initial pair comes into play, since the measurement will change the state of the other particle and this is what changes the probabilities to break the Bell inequality. Since this is the whole point of the experiment, maybe this should be mentioned explicitly? 146.52.8.96 (talk) 13:58, 15 August 2022 (UTC)
replies: text: I'm afraid you misunderstood it. As long as both Alice and Bob measure in the |0>, |1> basis the results will be the same as with a hidden variable with a value 00 or 11. Indeed that's not interesting at all. However, in the CHSH game they never measure both in the same basis. When Alice's input is x=0 and Bob's input is y=0, Alice measures in the |0>,|1> basis and Bob measures in the |0>,|1> basis rotated by \pi/8. When considering the three other possible input combinations (x=0,y=1, x=1,y=0, and x=1,y=1) their bases are similarly related and the mathematics is very similar, so the article appropriately skips over that. Tercer (talk) 18:01, 15 August 2022 (UTC)
thread_title:  Analysis of Optimal Quantum strategy 

message: The sentence The mathematical formalism of quantum mechanics predicts a maximum value for S of 2√2 (Tsirelson's bound),[4] which is greater than 2, and CHSH violations are therefore predicted by the theory of quantum mechanics. uses a flawed argument. The therefore is wrong. One must show that Tsirelson's bound is the BEST possible maximum or, by the same token, that the maximum of the Tsirelson bound is ASSUMED in a number of cases. It is not sufficient to merely demonstrate one bound. Both is, of course, true and can be done. So the result is fine but the line of reasoning does not live up to the standards of precision which are possible.
I agree with this. If I state a bound, such as "nothing travels faster than 3 times the speed of light," it does not logically follow that objects are predicted to travel up to 3 times the speed of light. If there is something else going on with Tsirelson's bound, can someone please elaborate, and correct this section accordingly? --Randallbsmith (talk) 17:53, 16 March 2023 (UTC)
replies: text: Yes, the logic was flawed. I added (as is shown in detail later in the article), that QM predicts a violation and that the Tsirelson bound is attained in QM (eg. for Bell states and suitable measurement settings). --Qcomp (talk) 12:39, 28 October 2023 (UTC)
thread_title:  Flawed Argument 

message: This article needs to attempt to communicate to non-experts. After understanding a flaw in the opening paragraphs based on confounding “no data” with a negative response I skipped pages devoted to a derivation as being beyond me. I was optimistic when I encountered the CHSH game but furious when the action of the third party was not described in terms I could comprehend or even type. YOU really need a section that is aimed at high school level. 67.170.237.132 (talk) 02:36, 4 February 2024 (UTC)
thread_title:  Please address a non-expert audience.