Is the Quantum Randi Challenge (QRC) valid?

[gill1109]

Why don't you setup the QRC in R and run the simulations thru it? It would be a good comparison. I'm quite busy enough for now learning Mathematica. I love it. Has some really great features.

Yes, Mathematica is fun, and can be useful.

QRC is a pedagogical tool. It could be set up in R. When I have my R Shiny server I will be able to set up an interactive R QRC webpage. Please be patient.

[gill1109]

Here's a first go at an R version of QRC:

http://rpubs.com/gill1109/QRC

[FrediFizzx]

No CHSH yet.

[gill1109]

No CHSH yet.

What do you mean? Do you want me to write out CHSH in the output as well?
Or do you mean, that I didn't succeed in violating CHSH (almost every time the experiment is run)?

[FrediFizzx]

You haven't put the QRC CHSH in the R program yet is what I meant.

[gill1109]

You haven't put the QRC CHSH in the R program yet is what I meant.

No, I hadn't bothered with that. Now I have added in a couple of extra lines calculating the actual and the theoretical CHSH value for this experiment: http://rpubs.com/gill1109/QRC

Notice that QM doesn't give 2 sqrt 2 but only 1 + sqrt 2, that's because we are not doing the optimal experiment from a CHSH point of view (we don't attain the Tsirelson bound). Vongehr prefers the original Bell three correlation inequality together with the requirement of perfect anti-correlation at equal settings, for pedagogical reasons. Actually I prefer CHSH.

Vongehr's Mathematica version required tables to be filled in. I prefer a "for loop" with one call of the three subroutines (one source and two detectors) in each of the 800 runs. I think it is more clear (pedagogical reasons, again) - the code is much easier to understand.

I plan to add some standard errors to the observed counts and correlations. Error bars. People need to realise that the final results are subject to statistical error, for two reasons: one, random choice of settings; two, random hidden variables in source and possibly also measurement stations. It is not enough to satisfy the QRC requirements just once. You have to violate Bell 99% of the time, and always have exact anti-correlation. 99% of the time means that 99% of repetitions of the whole experiment, every repetition has 800 new runs with 800 new random setting pairs.

The randomness in "my" finite sample version of the CHSH refers to the randomness in the settings. My inequality is probabilistic. Bell's inequality is an inequality about expectation values. Not about experimental averages.

[gill1109]

I've corrected some errors and added some standard errors.

Both for Vongehr's transformation of Bell's original three correlation inequality N1U <= N2E + N3U, and for the corresponding four correlation CHSH inequality rho3 - rho0 - rho1 - rho2 <= 2 .

http://rpubs.com/gill1109/QRC

You can see why a sample size of 800 is fine. Under QM (singlet state), CHSH would be 2.414... and the standard error (error bar) would be about 0.1. You won't often see an outcome four standard errors below the mean.

The mean value of N1U - N2E - N3U would be about 41.4 with a standard error of about 16.4.

You see why, statistically, it would be better to test with the CHSH quantity rather than with Vongehr's simple function of just three of the counts coming out of the experiment. However, for Vongehr's statistically weaker test, a sample size of 800 is also OK: you won't often see an outcome two and a half standard errors below the mean - it'll happen less than 1% of the time. He verified that error rate with a simulation experiment, I guestimated it with the central limit theorem.

[gill1109]

I posted the following announcement in several internet fora:

For those of you interested in winning the quantum Randi challenge, I've
posted an R script which you can use as basis for your own experiments,
http://rpubs.com/gill1109/QRC . You can read about the QRC in a number
of places, for instance in Sasha Vongehr's paper
http://arxiv.org/abs/1207.5294

R is free (both as in "free beer" and as in "free speech" and can be
obtained from http://R-project.org). It is the programming language of
choice for millions of data scientists throughout the world. It has a
steep learning curve but it pays off to try to climb the hill.

Your job is simply to program three functions which (a) generate hidden
variables for one particle pair at the source (b) compute a measurement
outcome at Alice's station, depending on Alice's setting, which will be
0 or 67.5 degrees, (c) compute a measurement outcome at Bob's station,
depending on Bob's setting, which will be 0 or 45 degrees. The outcomes
are binary (+/-1).

In the script, this is repeated 800 times; the settings being chosen
completely at random. After the experiment has finished, the data is
analysed. The aim is to have

(a) perfect anti-correlation when Alice and Bob have equal settings, and

(b) the number of times both their outcomes are unequal when their
settings differ by 22.5 degrees is larger than the number of time they
are equal when settings differ by 45 degrees plus number of times
unequal when settings differ by 67.5 degrees.

It is not too difficult to invent a local hidden variables theory which
always satisfies (a) and which satisfies (b) with probability half.
Probability half means: in half of the experiments. [Every experiment
has 800 runs, and two new, completely random, setting sequences.]

Quantum mechanics can in theory satisfy (a) always, and it can in theory
satisfy (b) in more than 99% of all experiments.

I remind you again: every experiment consists of exactly 800 runs.

If you win the experiment, don't tell me, but post your script on
internet. Of course the script must be legal, which means that it should
also run on separated computers and without knowing in advance what the
setting sequences will be. If, in such rigorous conditions, it does
indeed succeed, you have created a classical physical system (a
classical computer network) which exhibits quantum correlations
previously believed to be impossible to generate by classical means
without violating locality or arranging some kind of conspiracy. You
will very quickly become famous and win the Nobel prize for your
experimental disproof of Bell's theorem, and for the fact that you have
instantly destroyed the whole quantum entanglement business (quantum
computers, quantum communication, ...). No establishment conspiracy will
be able to stop you.

[FrediFizzx]

I am wondering if it is possible to not violate the Bell inequality and violate CHSH? It seems the QRC does that occasionlly. Is this a flaw? Here is the output from the QRC using the minkwe_reed Mathematica parameters.

"Anti-correlation at equal angles OK."
"Bell is not violated, try different HV."
{2.03158, "CHSH inequality is violated!"}

[gill1109]

I am wondering if it is possible to not violate the Bell inequality and violate CHSH? It seems the QRC does that occasionlly. Is this a flaw? Here is the output from the QRC using the minkwe_reed Mathematica parameters.

"Anti-correlation at equal angles OK."
"Bell is not violated, try different HV."
{2.03158, "CHSH inequality is violated!"}

Yes it is possible. It is easy to come up with LHV models such that Vongehr's Bell derived statistic is violated 50% of the time, and CHSH is violated 50% of the time. Vongehr looks at four absolute frequencies (one of which must be zero). CHSH in effect looks at four relative frequencies. The statistical errors in both are not 100% correlated.

My own script shows that CHSH is sharper: smaller relative error.

Is it a flaw? Vongehr thinks that his approach has pedagogical advantages. The usual CHSH has statistical advantages. Are we talking about a class-room demonstration, or a tool for professional experimentalists doing cutting edge experiments?

[gill1109]

Recall that QRC insists on perfect anti-correlation for one of the pairs of settings. So one of the four correlations in CHSH is -1. We are left with Bell's original three correlation inequality.

Now for the bridge to QRC. Each correlation can be written as ( N(==) - N(!=) ) / ( N(==) + N(!=) ). There are altogether 800 runs and the four setting pairs occur approximately equally often. So for each of the three not-necessarily-perfect correlations, N(==) + N(!=) is approximately equal to 200. Vongehr uses this approximation to reduce the Bell three correlation inequality to an inequality concerning three absolute frequencies of equality or inequality.

It is well known that ordinary people don't grasp probabilities very well, but do understand absolute numbers pretty well ... as long as they are not too large. So he has translated the mysterious correlation inequality into a simple statement about three counts, three numbers between 0 and (roughly) 200. One is smaller than the sum of the other two.

By demanding perfect anti-correlation for the equal setting case, it is clear that our LHV model can *only* have randomness in the source - there is no extra randomness in the measurement stations. This also makes the whole thing easier to think about.

These are pedagogical innovations, designed so that you can easily explain Bell to, e.g., high school students (and not just maths and physics high school students), in such a way that they really understand what is going on - they are not just hit over the head with fancy formulas. Science outreach.

[FrediFizzx]

Thanks for the explanation but we already knew all of that.

[gill1109]

Still wondering what you mean by the question "is QRC valid"? It seems to me easy to see that you can't win QRC - ie you can't write computer programs which generate certain results. It also seems to me easy to see that measurements on entangled quantum systems could, in theory, generate those results. Do you think that you can win the challenge? Or do you think that QM can't?

[FrediFizzx]

??? I believe I have already discovered a flaw in the QRC. Will report more when I am completely done with the analysis. So since it is flawed, then it is certainly not valid as a Bell HV model tester. I certainly hope that answers your questions.

[gill1109]

??? I believe I have already discovered a flaw in the QRC. Will report more when I am completely done with the analysis. So since it is flawed, then it is certainly not valid as a Bell HV model tester. I certainly hope that answers your questions.

If you are right, and when you have reported your finding, then my question will have been answered.

I am worried about a potential circular reasoning trap. Suppose we believe Joy's model is correct. Suppose we believe we have correctly implemented it as a local hidden variables computer simulation. We will discover that it cannot win QRC. You will say that this is proof that QRC is flawed. I will say this is proof that Joy's model is flawed.

The problem with being absolutely certain about anything, is that it prevents one from even seeing evidence that one's certainty is misplaced. It's very human, but it's an unscientific attitude.

[Mikko]

??? I believe I have already discovered a flaw in the QRC. Will report more when I am completely done with the analysis. So since it is flawed, then it is certainly not valid as a Bell HV model tester. I certainly hope that answers your questions.

Which kind of flaw? Are the requirements too restrictive or too permissive?

[FrediFizzx]

It looks to be too restrictive from first analysis.

[FrediFizzx]

And... My long awaited answer to the question that I first posed when I started this thread is that the QRC is not a valid Bell hidden variable model tester for all cases of possible hidden variable models. The reason why is that it basically excludes a certain class of hidden variable model since the angles for a and b are both zero for about 25 percent of the time. IOW, for approximately 200 out of 800 trials. The reason why the angles were chosen of 0 for a, 3pi/8 for a', 0 for b, and pi/4 for b' was to be able to do the anti-correlation in the same test. This proves to be the part that flaws the QRC.

For HV models like the ones that we have been discussing here for the computer simulations, having angles for a and b both being zero 25 percent of the time, renders a function like |cos(a - e)| > lambda and sign(-cos(a - e)) useless in a proper Bell test (same situation for b - e). Because those functions just become |cos(-e)| > lambda and sign(-cos(-e)) for 25 percent of the time. That is a pretty sizable flaw in the QRC of at least 25 percent error. As Joy put it in a private email, "A deliberate bias has been introduced, which is not there either in QM or in the actual experiments (let alone in my model)."

Now, when the QRC is modified to use the Weihs, et al, angles of 0 for a, pi/4 for a', pi/8 for b, and 3pi/8 for b' with proper adjustment to the appropriate formulas, hidden variable models of the class like above can violate Bell and CHSH all of the time. Of course the original QRC must be used to check for perfect anti-correlation since the anti-correlation check no longer works using the Weihs, et al, angles since we never have the angles equal in that situation.

And thanks go to John Reed for giving me the idea to try the Weihs, et al, angles in the QRC programming.

[gill1109]

And... My long awaited answer to the question that I first posed when I started this thread is that the QRC is not a valid Bell hidden variable model tester for all cases of possible hidden variable models. The reason why is that it basically excludes a certain class of hidden variable model since the angles for a and b are both zero for about 25 percent of the time. IOW, for approximately 200 out of 800 trials. The reason why the angles were chosen of 0 for a, 3pi/8 for a', 0 for b, and pi/4 for b' was to be able to do the anti-correlation in the same test. This proves to be the part that flaws the QRC.

For HV models like the ones that we have been discussing here for the computer simulations, having angles for a and b both being zero 25 percent of the time, renders a function like |cos(a - e)| > lambda and sign(-cos(a - e)) useless in a proper Bell test (same situation for b - e). Because those functions just become |cos(-e)| > lambda and sign(-cos(-e)) for 25 percent of the time. That is a pretty sizable flaw in the QRC of at least 25 percent error. As Joy put it in a private email, "A deliberate bias has been introduced, which is not there either in QM or in the actual experiments (let alone in my model)."

Now, when the QRC is modified to use the Weihs, et al, angles of 0 for a, pi/4 for a', pi/8 for b, and 3pi/8 for b' with proper adjustment to the appropriate formulas, hidden variable models of the class like above can violate Bell and CHSH all of the time. Of course the original QRC must be used to check for perfect anti-correlation since the anti-correlation check no longer works using the Weihs, et al, angles since we never have the angles equal in that situation.

And thanks go to John Reed for giving me the idea to try the Weihs, et al, angles in the QRC programming.

Seems to me you have successfully explained why your favourite class of hidden variables models fails QRC. What you call a bug is actually a feature. Why not use the angles which John Bell proposed in 1964? QRC is just Bell's original thought experiment.

But if you don't like Bell's originally suggested experiment, we can switch to the later CHSH version (which Bell also endorsed). On a new thread which I started a day or two ago, we are re-discussing CHSH. (Essentially a revival of your thread on a new CHSH inequality, though is not actually new at all).

Your favourite models fail CHSH too. So far, you have been exploiting the detection loophole. Well known tricks going back to Pearle (1970) and wonderfully expounded by Caroline Thompson (chaotic spinning ball model).

[FrediFizzx]

...
ROTFLMAO! The models are (a - e) and (b - e) not (0 - e) and (0 - e). 25 percent of the time, the QRC is testing a different model. It's a big flaw and fixable by using the Weihs' angles. Anyone can easily see that. And with Joy's proof of the connection to 3-sphere geometry, there is no problem with the class of models of that type.