Nick Herbert's Proof: Quantum Non-Locality Explained

[gill1109]

Herbert's proof is a proof of Bell's theorem by consideration of a two-party, two-setting, two-outcome experiment. In other words, a CHSH-style experiment. Every CHSH-style experiment which has been done to date, and which had a successful outcome (a violation of CHSH inequality) suffers from one of the "standard" loopholes, ie failure to comply with rigorous experimental protocol requiring timing, spatial separation, rapid generation of random settings, legal measurement outcomes. Every local-realistic simulation of the data of such an experiment has to exploit one of those loopholes. (Note that in the presence of perfect (anti)correlation in one setting pair, violation of Bell's original inequality and violation of CHSH inequality are equivalent).

 

[gill1109]

PS experts expect the definitive experiment within 5 years. Top experimental groups in Brisbane, Vienna and Singapore are very clearly systematically working towards this goal (whether or not they say so publicly), and no doubt others are in the race as well.

 

[lugita15]

Indeed, it doesn't have to be +30 degrees and -30 degrees; it think that +22 and -30 degrees is just as tough for "local reality"; his argument is not affected by that, I think.

Good, at least we're agreed on that.

However, many experiments used protocols that don't match Herbert's proof. Any one?

Just to be clear, by protocol do you mean his procedure of first aligning both polarizers, then tilting one until you get a certain error rate, then tilting it back and tilting the other one in the opposite direction until you get a certain error rate, and then tilting both in opposite directions? That particular procedure is as irrelevant as the choice of angles a, b, and c. What matters is that you tests the error rates for a and c, a and b, and b and c.

Any simulation that manages to reproduce real observations will do so by employing means to do so - and I would not know which means would not be called "loopholes" by some.

Fair enough, I think it's pretty clear what is and isn't a loophole. Let me ask you this: do the simulations you're examining exploit either the communication loophole or the fact that detection equipment is imperfect?

I'm interested to verify such simulations with experiments that have actually been performed; but regretfully, many experiments have built-in loopholes by design. Herbert's design of experiment contains perhaps the least pre-baked loopholes, and that makes it challenging. Thus, once more: has his experiment actually been done, as he suggests?

When you say "as he suggests", do you specifically want an experiment capable of testing his inequality? Well, his inequality can only be tested if you have 100% detector efficiency. (Otherwise you need the CHSH inequality.) The only experiment to date that achieved that was the ion experiment by Rowe, but that experiment didn't close the communication loophole.

Or do you want an experiment that tested the CHSH inequality instead, but used a more "Herbert-like" setup in whatever sense you mean it?

PS: please don't present excuses why such an experiment has (maybe) not been performed; only answer if you can fulfill my request and give such matching data

It's unclear what you want. If you're looking for a loophole-free Bell test, then we're still working on that.

 

[gill1109]

In Herbert's setup we know in advance that first we will first do a heap of (0,0) measurements then a heap of (0,30) and so on. If the number of each kind is fixed in advance then it's rather easy to come up with a LHV computer simulation which does the job exactly. Freedom loophole. If the numbers are not known, then you can easily do it if you also use the memory loophole.

I suppose someone who did Herbert's *experiment* wouldn't demand exactly zero error rate in the (0,0) configuration. They'd allow a small error rate. So in effect, test CHSH. CHSH looks at four orrelations. Fix one at +1, and you reduce it to Bell's inequality, which is essentially Herbert.

See arXiv:1207.5103 by RD Gill (me), I uploaded a revised version last night. It will be available from at Tue, 20 Aug 2013 00:00:00 GMT.

 

[harrylin]

[..] Just to be clear, by protocol do you mean his procedure of first aligning both polarizers, then tilting one until you get a certain error rate, then tilting it back and tilting the other one in the opposite direction until you get a certain error rate, and then tilting both in opposite directions? That particular procedure is as irrelevant as the choice of angles a, b, and c. What matters is that you tests the error rates for a and c, a and b, and b and c.

Yes, what matters for me is the kind of angles that are actually tested, as required for his proof. If there was a paper of an experiment that actually followed Nick Herbert's proof as protocol, then it would be easier to explain (and no need to explain). But apparently that hasn't been done...

Fair enough, I think it's pretty clear what is and isn't a loophole. Let me ask you this: do the simulations you're examining exploit either the communication loophole or the fact that detection equipment is imperfect?

No communication loophole is used, and the output signals at 0 degrees offset are 100% if that is what you mean. But this thread is not about simulation programs; my question is about Herbert's proof.

When you say "as he suggests", do you specifically want an experiment capable of testing his inequality? [..] Or do you want an experiment that tested the CHSH inequality instead, but used a more "Herbert-like" setup in whatever sense you mean it?

I ask for the data of an experiment that did what I put in bold face: with set-up I mean a protocol that matches his proof. Likely one or two were done that contain it as a subset. The program that I tested passed a CHSH test with flying colours (there could be an error somewhere of course!) but failed the protocol of Nick Herbert. As Herbert's test is much clearer and simpler, that's what I now focus on.

 

[harrylin]

Herbert's proof is a proof of Bell's theorem by consideration of a two-party, two-setting, two-outcome experiment. In other words, a CHSH-style experiment.

At first sight yes, but I found that details matter as much as they matter with magic tricks (that's one of my hobbies).

[...] I suppose someone who did Herbert's *experiment* wouldn't demand exactly zero error rate in the (0,0) configuration. They'd allow a small error rate. So in effect, test CHSH. CHSH looks at four orrelations. Fix one at +1, and you reduce it to Bell's inequality, which is essentially Herbert.

See arXiv:1207.5103 by RD Gill (me), I uploaded a revised version last night. It will be available from at Tue, 20 Aug 2013 00:00:00 GMT.

I'll have a look at that, thanks!

 

[gill1109]

You're asking for a CHSH style experiment where first one of the four pairs of angles is used for many runs, then a second pair, then a third, then a fourth. First (1,1), then (1,2), then (2,1), finally (2,2). And you want perfect correlation in the first batch of runs.

In a real experiment counting coincidences of detector clicks you'll never see *perfect* correlation if the number of runs is large. You might see near to perfect correlation. What will you do then? Publish a failed experiment?

 

[harrylin]

You're asking for a CHSH style experiment where first one of the four pairs of angles is used for many runs, then a second pair, then a third, then a fourth. First (1,1), then (1,2), then (2,1), finally (2,2). And you want perfect correlation in the first batch of runs.

In a real experiment counting coincidences of detector clicks you'll never see *perfect* correlation if the number of runs is large. You might see near to perfect correlation. What will you do then? Publish a failed experiment?

A set-up isn't an outcome of course, and a near to perfect correlation sounds good to me. However, publication bias as you suggest appears to be a serious problem nowadays... it's a serious risk also with Bell tests. Imagine that Michelson had not published his "failed" experiment!

 

[gill1109]

Yes, magic tricks! Every disproof of Bell's theorem whether theoretical or by computer simulation is based on a conjuring trick. Combination of sleight of hand, the gift of the gab. That's why the QRC (quantum Randi challenge) was invented.

 

[harrylin]

Yes, magic tricks! Every disproof of Bell's theorem whether theoretical or by computer simulation is based on a conjuring trick. Combination of sleight of hand, the gift of the gab. That's why the QRC (quantum Randi challenge) was invented.

Nick Herbert's experiment remains impressive to me, especially at high efficiency; it's perhaps stronger than CHSH. Some imagined loopholes are just nonsense that could distract the audience and even the experimenters themselves. Ever heard of the fakir who throws up a rope in the sky and disappears in the clouds? Apparently such things have been done, but as always, the real protocol was not exactly like that! I'm a bigger skeptic than Randi.

 

[gill1109]

Herbert has a proof, not an experiment.

The experiment corresponding to Herbert's proof would be a CHSH experiment with special choice of settings, applied in a special sequence (known in advance), and a more stringent criterium than "violate CHSH inequality". Herbert requires "violate CHSH inequality and get perfect correlation with the first of the four setting pairs".

So it is stronger in just once sense, but weaker in others.

 

[harrylin]

Herbert has a proof, not an experiment.

The experiment corresponding to Herbert's proof would be a CHSH experiment with special choice of settings, applied in a special sequence (known in advance), and a more stringent criterium than "violate CHSH inequality". Herbert requires "violate CHSH inequality and get perfect correlation with the first of the four setting pairs".

So it is stronger in just once sense, but weaker in others.

He makes a claim about physical reality based on experiments which supposedly proved that claim. The sequence plays no role in his proof; however the direct comparison of certain settings does (without mixing in other settings, which could obscure the interpretation). I'll check out your paper tomorrow to see if I can extract relevant data from it or its references.

 

[lugita15]

Yes, what matters for me is the kind of angles that are actually tested, as required for his proof.

What do you mean "the kind of angles"? Didn't you just agree with me that the logic of the proof is unaffected by what three angles you choose?

No I ask for the data of an experiment that did what I put in bold face: with set-up I mean a protocol that matches his proof. Likely one or two were done that contain it as a subset.

Sorry, when did you put something in boldface?

Can you tell me what would or would not count as a "protocol that matches his proof"? I don't even know what you mean by protocol. Do you mean that the experiment should measure the error rate for a and c, a and b, and b and c, or do you want something more demanding?

 

[harrylin]

What do you mean "the kind of angles"? Didn't you just agree with me that the logic of the proof is unaffected by what three angles you choose?

It's the details that matter, see below. Probably that has been done, but yesterday I didn't find such a data set (to my great surprise). Maybe tomorrow.

Sorry, when did you put something in boldface?

Post #97: I made "set-up" bold-face, to stress that I talk about how the test is done.

Can you tell me what would or would not count as a "protocol that matches his proof"? I don't even know what you mean by protocol. Do you mean that the experiment should measure the error rate for a and c, a and b, and b and c, or do you want something more demanding?

Hardly more demanding than that. Getting back to my reminder of yesterday:

'Step One: Start by aligning both SPOT detectors. No errors are observed.
Step Two: Tilt the A detector till errors reach 25%. This occurs at a mutual misalignment of 30 degrees.
Step Three: Return A detector to its original position (100% match). Now tilt the B detector in the opposite direction till errors reach 25%. This occurs at a mutual misalignment of -30 degrees.
Step Four: Return B detector to its original position (100% match). Now tilt detector A by +30 degrees and detector B by -30 degrees so that the combined angle between them is 60 degrees.'

From that I get that for his argument we need at detectors (A, B) data streams from the angle pairs (a a'), (b a'), (a c), and (b c) as a minimum, and it would be nice to repeat (a a') as Herbert suggests. As experimenter I would also throw in once (b b') and (c' c) for better characterization, but it's not necessary. Moreover, typically b and c are <45° angles in opposite directions but I suppose that bigger angles are also fine.

 

[harrylin]

[..] I suppose someone who did Herbert's *experiment* wouldn't demand exactly zero error rate in the (0,0) configuration. They'd allow a small error rate. So in effect, test CHSH. CHSH looks at four orrelations. Fix one at +1, and you reduce it to Bell's inequality, which is essentially Herbert.

See arXiv:1207.5103 by RD Gill (me), I uploaded a revised version last night. It will be available from at Tue, 20 Aug 2013 00:00:00 GMT.

Hi Gill, I now looked at your revised version. Does any of your references contain the data set(s) that I'm after??