Talk:CHSH inequality

1985:

the correlator is indeed 0.5. As for the lack of response you got, it's because this is the deadest of the dead horses. People have been trying for decades to violate a Bell inequality with a LHV model. It can't be done. After you found the mistake in a hundred different attempts, there's no energy anymore for going through the hundredth and one. I'm not going to read through Freedman's PhD thesis to figure out what is going on. I can remark that this is seriously obsolete stuff, there's no point in playing around with angles and spin and polarizers. The modern formulation of the CHSH inequality is the CHSH game, which is described in this very article. It is much simpler, with less room for confusion.

84: 1946:

0.448 0.993 0.4375 0.97 0.97 0.400 ± 0.007 22.5 0.401 1.003 0.375 0.935 0.935 0.340 ± 0.010 33.75 0.333 0.979 0.313 0.939 0.92 0.249 ± 0.007 45 0.251 1.008 0.250 0.996 1.004 0.164 ± 0.007 56.25 0.170 1.03 0.1875 1.10 1.14 0.100 ± 0.003 67.5 0.100 1.0 0.125 1.25 1.25 0.052 ± 0.004 78.75 0.055 1.058 0.0625 1.13 1.20 0.041 ± 0.003 90 0.039 0.951 0.000 100 100

596:, involving single-channel polarisers and subexperiments with polarisers removed. They said quite clearly that inequalities (1) (the CHSH inequality) could not be used in optical experiments ( the only kind envisaged) because of the low efficiency of photodetectors. There follows a rather indirect derivation of the CH74 inequality, using distincly confusing notation. '-' now means not the '-' channel of a two-channel analyser but non-detection in the single channel of a one-channel one, i.e. it would correspond to -1 or 0 if we had two channels. 1386:. 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. 2000:

course it is, the spin axis that they have has been thrown to the wind and allowed to fall in various combinations of parts of itself. Spinors are fail, they lose 50% of the angles. The assumptions of Bell and CHSH are that the hidden variable is digital ahead of time; I concur that this will not work, and a simple MC simulation with a better defined LHV can prove that. They say the first thing you hear you're more likely to believe, and this was my introduction to CHSH game theory

74: 53: 2065:). In fact, between 1971 and 1981 Bell has moved from a stochastic model to an essentially deterministic model. Since in nature we see apparent randomness which can be explained as deterministic chaos, there is no contradiction here, but rather a weakening of assumptions. The concept of local realism (local hidden variables) has become broader, the theorem has therefore become stronger. 1562:. The two curves are not exact, and I'm not claiming to disprove QM; but this does raise the lower limit of what a hidden variable can be. This hidden variable predicted correlation value intersects exactly with Bell's Inequality at Bell's Test Angle of 60 degrees; so if Bell's Inequality disproves hidden variables, then this should disprove badly defined (digital) hidden variables. 1011:. 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. 936:(which I am considering including) does not really need the assumption that you can multiply independent probabilities at all. All it needs is that the state of the complete system be unaffected by the polariser settings. This is generally the case in real experiments other than ones such as Rowe's "trapped ion" one, where everything, including "detector settings" could interact. 22: 162: 1027:... 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 ...) 971:

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?

1483:

tested with two remote friends, using an 'entangled PRNG' to generate a hidden variable I call 'spin axis'. This axis is then taken with a dot product of the detector alignment; the resulting probability is the ratio of overlapping/non-overlapping half-circles (or two quarter circles 180 degrees apart), and is

2007:

I gave up looking for additional information on R^3 3D rotation vectors, and have yet to stumble on any other adaptation of them as a term; and I've investigated all other systems (because that's all that there is out there to find), and they have deficiencies; linear algebra rational matrices do the

1923:

With a stack of polarizers, the only events that count are those that make it through both, vs the total amount that would normally be received with no polarizers in the same amount of time. If the photon passes the first polarizer, and since there is only a second polarizer, then it doesn't matter

970:

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

2256:

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

607:

But what that first page is really saying is something very simple: that we look for + and - outputs on both sides and clock up the appropriate "coincidence" counter when there are non-null observations. And I find the notation makes for very poor legibility. In any event, we can surely drop most of

2132:

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

1945:

experimental angle QM pred. QM/Exp LHV pred. LHV/QM LHV/ result Exp. Res. 0.457 ± 0.009 0.00 0.464 1.015 0.5 1.07 1.015 0.451 ± 0.013 11.25 (0.438)

1482:

Bell's Inequality and CHSH Inequality both propose that the local variable is itself already the outcome and is a digital +1/-1 type value. It's true that this sort of variable cannot exceed the proposed inequalities. I built this CHSH game implementation, which can be played alone, but could be

982:

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.

943:

article absolutely stultifying. Where did you get your ideas about Malus' from? I've recently been reading about his true work in Mach's "Principles of Optics" and you are definitely misrepresenting him. You are also, I think, misrepresenting John Bell if you associate his harmless discussion in

220:

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

2219:

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

1999:

Failures should be recorded also; I was shown a couple other failed ideas for LHV, of course they were failures based on failed ideas. I continued to search for experimental data, and ran across Bohmian Mechanics (pilot wave with De Broglie) but the section on entangled spin axis is blank; but of

1984:

The correlator is not measured in %, it's just a number between -1 and 1. If your variables are perfectly correlated you get 1, if they are perfectly anti-correlated you get -1, and if they are completely uncorrelated you get 0. In your example, if you get 75 equal results and 25 different results

1429:

in a slightly different formulation. I think a section explaining the game formulation would be a valuable addition to the current article. (Digressing a bit, the article confuses local randomness with shared randomness, and this must be corrected. I'm too busy now, but if nobody does it I'll take

1138:

Perhaps I just have to give up: the robot thinks the word "oriented" is preferable to "orientated", which it does not seem to have heard of. My "Word" spellchecker accepts both. Is there any way of persuading the robot I'm right? Despite what "Word" says, "oriented" is not part of my language.

576:

There must be an infinite number of thought-experiments that don't match the conditions! CHSH, though, were concerned with the *real* possibilities. I think that on this page we should restrict ourselves to just these, vis the ideal CHSH inequality as expressed in (1a) of the CHSH 1969 paper, or

2284:

is quite awful too. I think articles should talk about polarized light as polarized light and the actual properties thereof instead of abstract or analogous properties that result in statements that don't make sense/require faith. THEN generalize to other properties/example (e.g. electrons with

2215:

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

332:

In trying to reproduce any derivation (as far as is indeed reproducible at all) what we basically need (and have already) are careful definitions of the symbols used, of quantities to be measured experimentally, of distinctions to be denoted; together with the complete statement of the conditions

615:

That would be neglecting the important class of OLTs for which the hidden variable does vary trial by trial, for which the trial index j consequently is appropriate to denote the system state, of which the assumption of distribution ρ being the same for all subexperiments cannot be made, and for

1894:

which makes the a+b go away. In the case of Bells test values; at 60 degrees, (a-b)/(a+b) means in 100 samples with 75 correlated and 25 decorrelated is 50%? I recognize this isn't a forum, and don't mean to start debate; I've posted a few places and not gotten meaningful feedback(positive or

2027:

I added this section with a better explanation of my correlator. The short of it is for a sequence of (S)ame and (D)iffering results, as known already from the counts of all inputs; but really as considered as a string of results "SDSDSDSDSD"; at 90 degrees, you get as many correlations as

822:

The Tsirelson Inequality surely deserves its own article. Its relevance here is of course that it is of a similar form as the CHSH inequality, but weak enough to be satisfied by all OLTs. This can be referenced for instance per M. A. Nielsen, I. L. Chuang, "Quantum Computation and Quantum

2031:

count the length of the chain, so 'SS' is 1, or I reset the counter every time the state of same and different changes to 0, and increment if the next is still the same. There's a total of 2 same correlations, and only 1 in a chain, resulting in 50% correlation. The math ends up like

1196:

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.

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The indicated emphasis is evident in title of reference: "Proposed Experiment to Test ...", PRL23, 880 (1969), as well as in statements therein, such as "The aim of this paper is to propose explicitly such an experiment." or " the condition for violation of Inequality (2b) is (4).

397:

Quote some of what Clauser et al actually wrote in 1969, 1974 and 1978 re use of the inequality, making it clear that in 1969 what they in fact recommended was the CH74 inequality, only with a rather clumsy derivation that implied the latter needed assumptions that are in fact

983:

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).

1812:; this makes an experiment with 99 runs and 66 correlations and 33 non-correlations have a 50% correlation; every other correlation is a good one. What happened to the (a+b) is that I took the ratios of (actual correlations to the total) to (correlations to the total) 1178:"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." 2004:. I didn't find 'Freedman's PHD Thesis' only 'Feynman's...' which is 20 years before bell; speaking of years, most of these experiments have been done within my lifetime; mind you I was a kid for a lot of those; but, if you think it would help I'd give it a lookover. 2154:

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:

724:... But whoever lets statements about "non-detections" appear in articles, such as Bell's 1971 eq. (6), needs to be very careful to point out all related assumptions, such as Bell's 1971 eq. (10), and to avoid generally false assertions such as Bell's 1971 eq. (12). 253:

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

1119:, 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 513:

But whoever lets statements about "non-detections" appear in articles, such as Bell's 1971 eq. (6), needs to be very careful to point out all related assumptions, such as Bell's 1971 eq. (10), and to avoid generally false assertions such as Bell's 1971 eq.

1104:

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.

1079:

I've replaced the whole page as promised. It's rather different! I cover all the functionality of the original and more, except that I've left out all mention of the Tsirelson Inequality, which is both irrelevant and based on nonsensical assumptions.

1217:'...The constraint but can on the other hand be infringed by quantum mechanics....' . . The intended meaning of this sentence is elusive. . I know 'butt-can' wasn't intended or any better, but it is the only thing that comes close to making sense. 409:* To point out consequences of the derivation (and the corresponding thought experiment) itself, i. e. in particular the class(es) of "objective local theories (OLT)" which don't satisfy the conditions under which the inequality can be derived; and 2060:

The article gives Bell's 1971 proof. It is thought to be more complicated than other proofs, and it makes physical assumptions which Bell himself later discarded. I think the article should add a section on Bell's 1981 proof (Bertlmann's socks,

1101:, 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. 572:... point out consequences of the derivation (and the corresponding thought experiment) itself, i. e. in particular the class(es) of "objective local theories (OLT)" which don't satisfy the conditions under which the inequality can be derived; 689:" denotes the (complete) system state in (at least) one particular trial of set J, then it is assumed that in (at least) one trial of set K (disjoint from set J) a completely equal system state occured, which is equally to be denoted by "λ 1924:

if the first polarizer modifies the result, it would still be in the same arc as the original input. This makes the probability of making it through both polarizers (pi/2 - x ) / pi for x in radians. (90-x)/180 for x in degrees...

651:

is most of all an adequately self-contained derivation of the CHSH inequality; with applications and relation to other articles and topics mentioned and linked, for instance (why not?!), according to your suggestions below, to

731:"Unfortunately, if the particles are optical photons (as in the experiment proposed below) no practical tests of (1) can presently be performed in this way, because available photoelectric efficiencies are rather small ..." 762:

to the derivation of the CHSH inequality (1b). The possible consideration of (non-unity) "efficiencies" and "non-detections" is contingent on interpretation of what's to be counted (and perhaps appropriately addressed in

1892: 2009:

pi rotations). I doubt you could name an approach I haven't already heard of. Although rotation vectors can be made into all those other things, that doesn't help the situation; that just breaks what already works.

2235:

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).

2187:. 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. 1054:

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 ...

2209:

The mathematical formalism of quantum mechanics predicts a maximum value for S of 2√2 (Tsirelson's bound), which is greater than 2, and CHSH violations are therefore predicted by the theory of quantum mechanics.

2084:. Your help in fixing it is very much appreciated. I would just delete the Bell 1971 proof, it's obsolete. The proof by CHSH 1969 is much better. Bell 1981 is also fine, although that's not my favourite proof. 497:

appropriate to denote the system state, of which the assumption of distribution ρ being the same for all subexperiments cannot be made, and for which the CHSH inequality (among others) can consequently not be

1046:

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

2082:

the only assumptions really needed for the inequality itself (as opposed to the method of estimation of the test statistic) are that the distribution of the possible states of the source remains constant

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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?

999:

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.

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My 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

603:

On the contrary: without careful definition in terms of experimental procedures and values (here: counts) we have no experimental test at all; nor any scientific/falsifiable theory to begin with.

510:

We don't need ... to be limited to just one derivation; inequalities which are known by distinct names and/or which were published by distinct sets of authors generally deserve separate articles.

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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?

612:

We don't need to even define ρ(j), since it is assumed that the distribution of ρ is the same for all subexperiments. The ρ that we are interested in is a function of the hidden variable, λ.

481:

We don't need to even define ρ(j), since it is assumed that the distribution of ρ is the same for all subexperiments. The ρ that we are interested in is a function of the hidden variable, λ.

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The mistake you made is the definition of correlator. It is the probability of getting equal results minus the probability of getting different results, or in the case of an estimator,

1063:

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").

991:

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".

834:

I strongly disagree; however, the derivation as sketched presently is quite simplistic ... although, thereby, it may not violate any copyright per Lett. Math. Phys. 4, p. 93, (1980) ...

313:

Reproduce the approved "derivation", which is not the original CHSH 1969 one but Bell's 1971 version (reproduced in Clauser and Shimony's 1978 report, pp 1892-1893, or p 37 or p 156 of

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BTW you've completely misrepresented Malus! I've put a comment on the discussion page, though wikipedia doesn't seem to think the article exists. Also I find your notation in the

953:

I've just checked Shimony's article: his derivation does not seem to be correct. A pity. I'll revert to using John Bell's 1971 one unless I can find out how to correct Shimony's.

749:"We shall therefore henceforth interpret A( a ) = +/- 1 and B( b ) = +/- 1 to mean emergence or nonemergence of the photons from the respective filters detection or nondetection " 457:

Also, whether "non-detections" and associated assumptions have any relevance at all, depends on the definition of the quantities in terms of which the CHSH inequality is derived.

1447:

per the above. As it stands, having two separate articles on topics that are so closely related doesn't make sense. At some future date, we might want to split material off of

995:

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

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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?

1015:... 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. 426:

It is named for the authors, John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt, of the paper in which this inequality was first derived, and where its

1067:

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.

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We don't need any of the first page: it is absurd to introduce something that was designed to test hidden variables in any other way than in terms of hidden variables!

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As part of a whole series of articles on related topics, within an encyclopedia, the article should use notation distinctly, consistenly and carefully; e. g. (ideally)

577:

the equivalent more symmetrical form -2 <= S <= 2, but in the more general form proved by Bell, 1971, in which non-detections are allowed for. Since CHSH did

401:

Mention some of the experiments in which the CHSH inequality has been used, and the typical reservations regarding the fair sampling/detection/efficiency loophole.

2080:

The problem is that this article was written mostly by a crackpot, Caroline Thompson. It is not only weird, but sometimes outright false, such as this quotation:

140: 978:... 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 ? 1319:

Please consider incorporating material from the above draft submission into this article. Drafts are eligible for deletion after 6 months of inactivity. ~

439:

The indicated emphasis is evident in title of reference: "Proposed Experiment to Test ...", PRL23, 880 (1969), as well as in statements therein, such as

1039:

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!

465:

of the first page: it is absurd to introduce something that was designed to test hidden variables in any other way than in terms of hidden variables!

696:

Yes, this assumption is not only relevant in some actual experiments, but it is essential for deriving the CHSH inequality itself in the first place.

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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.

841:

Other inequalities, such as the trivial one variously attributed to D'Espagnat, Wigner or whoever, discussed in Bell's "Bertlmann's socks" article (

130: 522:

The Tsirelson Inequality surely deserves its own article. Its relevance here is of course that it is of a similar form as the CHSH inequality, but

412:* To point out the advance of CHSH, especially over Bell, Physics1 (1964), eq. (15), e. g. by obtaining the latter as a special case of the former. 1815: 518:

We don't need even to mention the Tsirelson Inequality, which I for one have never heard of and which has never been applied in any experiment.

450:

If such emphasis and suggested decisiveness was modified in later publications, then this ought to be mentioned, of course; thus approaching a

530:

OLTs. This can be referenced for instance per M. A. Nielsen, I. L. Chuang, "Quantum Computation and Quantum Information", Cambridge UP (2000).

83: 1155:, 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? 2127:

In the case of the 3 other possible input pairs, essentially identical analysis shows that Alice and Bob will have the same win probability

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max(S,D)-min(S,D)/max(S,D). I did also find Bell's original paper, and in (10) he says the value is (-1+2/pi x) which is a linear line.

1425:, the topic of the CHSH nonlocal game is notable enough for a standalone article, but as it is the article merely duplicates content from 1460: 1008: 593: 391: 1218: 279: 2130:

But this seems to be skipping over the most interesting part: If I understand correctly, as long as Alice still measures in the |0: -->

785:

I was under the impression that our discussion so far only dealt with "non-detections" in the latter sense, i. e. with trials in which

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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?

2328: 2134: 445:" the condition for violation of Inequality (2b) is (4). This is the essential requirement on the design of a decisive experiment." 1307: 1007:

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

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2. "non-detection with a single-channel detector" is a notion quite different from "non-detection with a two-channel detector" ...

469:

On the contrary: without careful definition in terms of experimental procedures and values (here: counts) we have no experimental

581:

in fact recommend this test for practical use (see below), but instead the CH74 test we can scarcely avoid mentioning the latter.

1895:

negative). I appreciate your response; and that I named that paper 'theory' was a regret when I posted it here; it's just math.

1937:

Below is the experimental results from the link above, and new LHV predictions to relate... it's not far off? not CHSH 2 range?

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Under the described assumption, yes. ρ( j ) appears of course in the definition of "P" as experimental quantity, as the simple

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1. CHSH seem to go on to consider accumulative "rates" rather can sets of distinct, separate, single-photon-pair trials; and

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Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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and the probability of the state λ can be specified by a single function ρ(λ) that does not vary between subexperiments.

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But the assumptions behind it have no physical meaning! If it's not used anywhere surely it does not deserve a mention?

33: 674:(... presumably in "sufficiently large ensembles" or "over sufficiently (though necessarily finitely) many trials" ...) 1716:

to discuss your theories. There are plenty of websites for that, such as Physics Stack Exchange or Reddit AskScience.

806:

I have to be more precise: In question is the statement immediately preceding (12) that "P( a, b )) is given" by (12)

322:

I agree that the derivation(s) presented in the article may draw on several sources (of course in compliance with the

1659: 2286: 2276:"Then, it can randomly take either all the black the pair of balls has access to, or can show itself to be white" - 1530:

as a 'classical correlation prediction' vs QM's predicted correlation as just the dot product of the detectors of

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03:41, 2 Aug 2004 (UTC)) Yes, a few words of introduction seem appropriate, such as those in the present article.

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Is wikipedia's policy of a "Neutral point of view" suppose to mean the blatant suppression of a minority one?

644:

What we need here is to follow as succinctly as possible the evolution of the CHSH test as used in practice.

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I'm not clear from reading this. Should incidences be counted as +1, -1 or should they be counted as +1, 0?

1160: 263: 2138: 1003:... neither do they appear decisive about how to obtain the number "N", the "number of emissions" itself. 1422: 1140: 1106: 1081: 1072: 954: 947: 909: 634: 557: 534: 523: 2008:

job, but they don't have the information to do every job (they lose half the rotation space that's : -->

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Dr Chinese, your wholesale elimination of refs to my Chaotic Ball paper and pruning out of links to the

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Anyway, what I think we need to do is create a completely new page, perhaps with title "CHSH Bell test"

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Yes, I remember Caroline! She was well-meaning and she did identify issues with the early experiments.

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Re notation: I find all the little arrows make for far poorer legibility than the traditional + and -.

2106: 2070: 1712:, which is why you're getting nonsensical results. I'd like to remind you, though, that Knowledge is 1202: 1152: 506:, λ) that take values +1 or -1 but Bell's 1971 "A bar", the mean value, allowing for non-detections. 229: 1124: 21: 2290: 1313: 1182: 1120: 1094: 233: 1451:

if some individual section becomes overburdened, but that's not really the situation we face now.

105:

on Knowledge. If you would like to participate, please visit the project page, where you can join

2221: 1713: 1566: 1156: 932:

I'm working on a "CHSH Bell test" page, but have come across a difficulty! As far as I can see,

817:

The whole purpose of Bell's theorem is to show that the local realist prediction differs from it.

259: 1906:

Edit: There is a CHSH stacked polarizer experiment listed on one of the bell's experiment pages

181:

on 2022-03-13. For the contribution history and old versions of the redirected page, please see

1409: 1391: 1364: 213:

May I suggest also to include criticism on the completeness of the CHSH. To be found at: link

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I have seen the formula you use ("ArcCos") elsewhere, but that does not make it meaningful.

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it certainly underscores the importance of CHSH's suggestions as thought experiments ...

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As explained above, there is absolutely no problem here. And just why you think angles

889:

I strongly disagree; those topics are quite distinct, though closely related, of course.

728:

Non-detections have been there from the start. CHSH 1969 paper, last para of page 881:

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more details on different derivations may be spelt out in separate dedicated articles.

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line of reasoning does not live up to the standards of precision which are possible.

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Consequently the separate consideration of OLTs which don't satisfy this assumption.

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That would be neglecting the important class of OLTs for which the hidden variable

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if the definition of "P( a, b )" involves "non-detections" (in the latter sense).

671:

they assume the source always produces the same distribution of possible states,

2305: 2287:

https://physics.emory.edu/faculty/brody/Advanced%20Lab/entanglement%20manual.pdf

2188: 2085: 1986: 1717: 1431: 214: 73: 52: 2001: 886:

then if this looks an improvement the old CHSH inequality page can be dropped.

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https://github.com/d3x0r/STFRPhysics/blob/master/LHV_Theory.md#scoring-in-game

2011: 1969: 1954: 1571: 79: 255: 1379: 1320: 2304:

Can you be specific about which part of this article are you objecting to?

1887:{\displaystyle {\frac {\frac {a-b}{a+b}}{\frac {a}{a+b}}}={\frac {a-b}{a}}} 616:

which the CHSH inequality (among others) can consequently not be derived.

333:

required to derive (or, indeed, prove) the inequality under consideration.

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Right. A new project! I hope to get around to this, later this summer.

442:"The aim of this paper is to propose explicitly such an experiment." or 102: 803:

Incidentally, Bell's eq. (12) of his 1971 paper is the QM prediction.

2280:. This isn't even English, let alone correct. The language here/at 222:

2 | using LHV} is nonzero for quartets (1,1),(1,2),(2,1) and (2,2).

2278:

https://www.nobelprize.org/prizes/physics/2022/popular-information/

1908:

https://escholarship.org/content/qt2f18n5nk/qt2f18n5nk.pdf?t=p2au19

1115:

All other than Caroline: the substance of the debate on this is at

866:(Which would be an awful lot more than what's being menitioned ...) 633:

06:05, 4 Aug 2004 (UTC)) Surely eventually. More immediately, the

899:

Is there some way of creating a temporary page to develop it on?

347:(etc.) to denote and reference distinct detector systems (a.k.a. 470: 451: 1023:

in fact some non-detections. Clauser et al were aware of this.

961:

What CHSH really proved (and more on the Chaotic Ball geometry)

390:

Mention the fact that it can alternatively be derived from the

1567:

https://github.com/d3x0r/STFRPhysics/blob/master/LHV_Theory.md

156: 15: 2028:

non-correlation, and 0% correlation. with "SSDSSDSSD" I only

944:

the Bertlmann's socks article with your calculated cosines.

286:

to re-write the whole article! What we need is basically:

1649:{\displaystyle {\frac {N_{=}-N_{\neq }}{N_{=}+N_{\neq }}}} 1213:..The constraint but can on the other hand be infringed.. 1097:

page has surely overstepped the mark! Can't we please be

563:

Frank, I agree with many of your points. Exceptions are:

902:(By wikifying the term as article name; as I did above.) 845:, pp 139-158) could be mentioned somewhere in wikipedia 620:

If such OLT's exist they need to be on a separate page.

406:

I add (what's already indicated in the present article):

221:

S=E(1,1)-E(1,2)-E(2,1)-E(2,2), and Probability{|S| : -->

1480:

https://d3x0r.github.io/STFRPhysics/math/CHSH_Game.html

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The game has links at the bottom to more information;

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https://cds.cern.ch/record/142461/files/198009299.pdf

1818: 1805:{\displaystyle {\frac {\pi -x-x}{\pi -x}};a=pi-x;b=x} 1736: 1662: 1591: 1536: 1489: 1243: 1241: 1910:

which pages 83-85(ish) are the experimental results.

1348:

Subsequent comments should be made in a new section.

637:

ought to define them more explicitly and separately.

101:, a collaborative effort to improve the coverage of 666:(... at least in some, which may be referenced ...) 2179: 1886: 1804: 1704: 1648: 1554: 1522: 1284: 767:); it's not part of the derivation of (1b) itself. 647:No: what's needed here (according to the title of 1705:{\displaystyle {\frac {N_{=}-N_{\neq }}{N_{=}}}} 477:any scientific/falsifiable theory to begin with. 369:* avoiding the use of operator symbols (such as 489:vary trial by trial, for which the trial index 1351:A summary of the conclusions reached follows. 8: 2148:I'm afraid you misunderstood it. As long as 2002:https://qubit.guide/9.3-chsh-inequality.html 1285:{\displaystyle {\displaystyle E(a,b)}E(a,b)} 428:utility for experimental test was emphasized 215:http://dx.doi.org/10.1016/j.rinp.2014.06.002 187:; for the discussion at that location, see 2339:B-Class physics articles of Mid-importance 256:https://doi.org/10.1016/j.rinp.2015.06.002 47: 2169: 2164: 1866: 1819: 1817: 1737: 1735: 1694: 1683: 1670: 1663: 1661: 1637: 1624: 1612: 1599: 1592: 1590: 1535: 1499: 1488: 1242: 1240: 358:* denoting counts (natural numbers) with 776:Also, there are two complicating issues: 274:Suggestion for re-write of whole article 1523:{\displaystyle 1-({\frac {x}{\pi -x}})} 975:To take (some of) your points in turn: 49: 19: 2081: 2289:seems better than what we have here. 2272:Gibberish at NobelPrize.org and here. 2252:Please address a non-expert audience. 2157:basis and Bob measures in the |0: --> 385:) as mere distinct indices or labels. 7: 2220:correct this section accordingly? -- 2152:Alice and Bob measure in the |0: --> 2119:Analysis of Optimal Quantum strategy 1475:CHSH Game Implementation scores 3.40 1342:The following discussion is closed. 823:Information", Cambridge UP (2000). 95:This article is within the scope of 859:but there's no point in mentioning 420:need are false statements such as: 38:It is of interest to the following 1730:you're right, rephrasing it is... 1355:The result of this discussion was 1292:is then calculated as: (see Eq. 3) 14: 1151:I just added this article to the 677:... where the diversity of (all) 278:Hi Franck I've just been reading 2056:CHSH proofs: why stop with 1971? 1466:The discussion above is closed. 852:, as named in Bell's article ... 592:Yes, but inequality (2b) is the 160: 82: 72: 51: 20: 2334:Mid-importance physics articles 135:This article has been rated as 1656:. You are calculating instead 1549: 1543: 1517: 1496: 1279: 1267: 1259: 1247: 1235:The experimental estimate for 740:correct, FWIW, and followed by 324:GNU Free Documentation License 204:Talk:CHSH inequality/Archive_1 1: 1461:18:24, 5 September 2021 (UTC) 1440:15:27, 5 September 2021 (UTC) 1414:10:41, 5 September 2021 (UTC) 1396:10:35, 5 September 2021 (UTC) 1165:14:13, 11 December 2008 (UTC) 268:23:43, 23 February 2023 (UTC) 115:Knowledge:WikiProject Physics 109:and see a list of open tasks. 2267:02:36, 4 February 2024 (UTC) 2246:12:39, 28 October 2023 (UTC) 2211:uses a flawed argument. The 2123:The article currently reads 1308:07:45, 3 November 2020 (UTC) 1227:17:54, 4 February 2013 (UTC) 941:Wigner-d'Espagnat inequality 850:Wigner-d'Espagnat inequality 377:) or number values (such as 293:A few words of introduction. 118:Template:WikiProject Physics 2314:06:18, 1 October 2024 (UTC) 2299:05:44, 1 October 2024 (UTC) 2197:18:01, 15 August 2022 (UTC) 2143:13:58, 15 August 2022 (UTC) 1421:As I had written before in 1134:Robot spelling "correction" 502:We don't need functions A(a 289:What we need is basically: 246:10:14, 18 August 2014 (UTC) 2355: 2230:17:53, 16 March 2023 (UTC) 1430:care of it in two weeks). 1369:21:36, 13 March 2022 (UTC) 1329:15:40, 5 August 2021 (UTC) 796:(A↓) = 0" were counted ... 526:enough to be satisfied by 141:project's importance scale 1109:21:45, 31 Jan 2005 (UTC) 1084:09:17, 14 Aug 2004 (UTC) 1075:09:22, 29 Jul 2004 (UTC) 843:Speakable and Unspeakable 537:21:36, 29 Jul 2004 (UTC) 315:Speakable and Unspeakable 134: 67: 46: 2329:B-Class physics articles 2111:14:08, 28 May 2022 (UTC) 2094:12:46, 28 May 2022 (UTC) 2075:04:47, 28 May 2022 (UTC) 2042:10:38, 30 May 2022 (UTC) 2020:22:09, 29 May 2022 (UTC) 1995:08:11, 29 May 2022 (UTC) 1978:00:00, 29 May 2022 (UTC) 1963:07:30, 29 May 2022 (UTC) 1726:13:06, 28 May 2022 (UTC) 1580:02:55, 28 May 2022 (UTC) 1468:Please do not modify it. 1345:Please do not modify it. 1207:19:08, 5 June 2012 (UTC) 1191:15:42, 30 May 2011 (UTC) 1143:5 July 2005 09:10 (UTC) 1127:22:27, 31 Jan 2005 (UTC) 957:10:13, 4 Aug 2004 (UTC) 950:10:09, 4 Aug 2004 (UTC) 912:18:50, 2 Aug 2004 (UTC) 681:is taken to include any 1555:{\displaystyle \cos(x)} 925:06:05, 4 Aug 2004 (UTC) 792:(A↑) = 0" as well as "n 560:18:44, 2 Aug 2004 (UTC) 551:03:41, 2 Aug 2004 (UTC) 2181: 2180:{\displaystyle \pi /8} 1888: 1806: 1706: 1650: 1556: 1524: 1286: 685:diversity; i. e. if "λ 663:In actual experiments 28:This article is rated 2182: 1889: 1807: 1707: 1651: 1557: 1525: 1287: 167:The contents of the 2163: 1816: 1734: 1660: 1589: 1534: 1487: 1239: 1153:list of inequalities 1147:List of inequalities 934:Shimony's derivation 339:* reserving letters 282:and realised that I 198:Preceding Discussion 1378:I propose to merge 1314:Draft:The CHSH Game 1121:Bell test loopholes 1117:talk:Bell's theorem 1095:Bell test loopholes 98:WikiProject Physics 2177: 1884: 1802: 1702: 1646: 1552: 1520: 1282: 1262: 758:Note that this is 34:content assessment 2159:basis rotated by 1882: 1861: 1860: 1844: 1767: 1700: 1644: 1515: 1404:, per proposal.-- 1141:Caroline Thompson 1107:Caroline Thompson 1082:Caroline Thompson 1073:Caroline Thompson 955:Caroline Thompson 948:Caroline Thompson 910:Caroline Thompson 679:"possible states" 558:Caroline Thompson 535:Caroline Thompson 249: 232:comment added by 195: 194: 155: 154: 151: 150: 147: 146: 2346: 2186: 2184: 2183: 2178: 2173: 1893: 1891: 1890: 1885: 1883: 1878: 1867: 1862: 1859: 1845: 1843: 1832: 1821: 1820: 1811: 1809: 1808: 1803: 1768: 1766: 1755: 1738: 1711: 1709: 1708: 1703: 1701: 1699: 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