Can local hidden variable models handle Hardy's paradox?

[Jarek]

It seems many people here treat seriously possibility of local hidden variable models evolving in past -> future manner.
Beside issues with Bell inequalities, there are more problems with such view, like Hardy's paradox: https://en.wikipedia.org/wiki/Hardy%27s_paradox
Here is a nice diagram from Pawel Blasiak slides ( https://www.dropbox.com/s/jd7fixmpbyqb6 ... 8PB%29.pdf ):



You need to choose A_a and B_b functions of hidden variable lambda, such that |11> on 'z' is forbidden, but all other possibilities have nonzero probability - how to do it?
Observe that this paradox does not work in time-symmetric view like TSVF ( https://en.wikipedia.org/wiki/Two-state ... _formalism ): e.g. hidden local variables can come from both time directions to provide required dependence on the choice of second measurement.

[Joy Christian]

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There is no "Hardy's paradox." All sixteen predictions of the Hardy state have been reproduced exactly by my local-realistic S^3 model: https://arxiv.org/abs/0904.4259 (see Section V-A).

My paper is also published as Chapter 6 in the Second Edition of my book shown below. Since all sixteen predictions are reproduced local-realistically, there is no Hardy's paradox to address.

In fact, my comprehensive local-realistic S^7 framework, published by Royal Society, reproduces ALL quantum correlations local-realistically, no matter what the underlying quantum state.


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[Jarek]

Thank you, I will take a closer look.
If you believe you have a working local hidden variable model, why don't you simulate quantum algorithms in polynomial time - especially Shor's factorization?

[Joy Christian]

Thank you, I will take a closer look.
If you believe you have a working local hidden variable model, why don't you simulate quantum algorithms in polynomial time - especially Shor's factorization?

Several simulations of my model already exist on this forum. Some of them are discussed also on my blog and on my RPubs pages: http://rpubs.com/jjc. Two simulations based on the GAViewer are also included in my Royal Society paper: https://royalsocietypublishing.org/doi/ ... sos.180526. So plenty of simulations of my local-realistic 3-sphere model already exist.

Ultimately, however, I am not interested in any algorithms, computer simulations, or Shor's factorization. The problem of local realism is an analytical physical problem which no computer simulation can address adequately. Simulations are of course pedagogically useful and give good insights into the physical problem, but they cannot replace either actual physics or even analytical mathematics. And they most certainly do not render obsolete the need for doing actual experiments for studying Nature.

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[Jarek]

Quantum algorithms, especially Shor, are the ultimate test.
If you can effectively simulate them avoiding exponential cost of superposition, you will take all the spotlight from this currently huge field, immediately convince everybody, enforce rapid replacement of used cryptography ...
If you cannot, then your hidden variable is still missing something - might handle simple cases, but does not generalize.

[Joy Christian]

Quantum algorithms, especially Shor, are the ultimate test.

I disagree. Quantum algorithms do not have much to do with physics. They are more like a video game --- confined to the machines they are within, and oblivious to the reality of Nature.

If you can effectively simulate them avoiding exponential cost of superposition, you will take all the spotlight from this currently huge field, immediately convince everybody, enforce rapid replacement of used cryptography ...

I am not interested in being in the spotlight of any field. I am only interested in understanding Nature. If that means the entire physics community ignores me and my work, then so be it.

If you cannot, then your hidden variable is still missing something - might handle simple cases, but does not generalize.

It is not my hidden variable that is missing something. It is the algorithm-based ideology that is missing something. What it is missing is the geometry and topology of the physical space in which we are confined to perform all our experiments. My model explicitly takes those into account and succeeds, in principle, in reproducing All quantum mechanical correlations, no matter what the underlying quantum state.

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[Jarek]

Quantum algorithm is just an experimental setting combining multiple quantum operations - would allow you to prove that your model not only works in a few small customized settings, but also for complex ones built of combined multiple operations.
For this purpose you only need to express a few simple quantum gates ( https://en.wikipedia.org/wiki/Quantum_logic_gate ) and you can build e.g. Shor from them.
The big question is if it can be done using only local hidden variables, like your Bloch-like spheres?
How would you express especially C-NOT gate with your model?

I was a naive local hidden variable believer a decade ago, but broke my teeth on Shor: you split the calculation into two branches, provide input in one branch, read output for this input from second branch - to classically simulate it without superposition, you would need retrocausality: https://physics.stackexchange.com/quest ... its-crippl
I and many others would be extremely interested if you could handle this problem with your model, it would just end the quantum mysticism.

[Joy Christian]

Quantum algorithm is just an experimental setting combining multiple quantum operations - would allow you to prove that your model not only works in a few small customized settings, but also for complex ones built of combined multiple operations.
For this purpose you only need to express a few simple quantum gates ( https://en.wikipedia.org/wiki/Quantum_logic_gate ) and you can build e.g. Shor from them.
The big question is if it can be done using only local hidden variables, like your Bloch-like spheres?
How would you express especially C-NOT gate with your model?

As I noted, I am not interested in quantum algorithms or the C-NOT gate. They have little to do with physics. As long as they avoid the geometry and topology of the physical space, they are no more than a video game.

I was a naive local hidden variable believer a decade ago, but broke my teeth on Shor: you split the calculation into two branches, provide input in one branch, read output for this input from second branch - to classically simulate it without superposition, you would need retrocausality: https://physics.stackexchange.com/quest ... its-crippl
I and many others would be extremely interested if you could handle this problem with your model, it would just end the quantum mysticism.

My model has already ended quantum mysticism decisively. It has identified the raison d'être of strong correlations and reproduced ALL quantum correlations local-realistically in principle.

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[Jarek]

In physical realizations these gates are realized by physical processes:
https://en.wikipedia.org/wiki/Quantum_c ... alizations
I assume you are not able to realize it with your model, but it would be great if you could show otherwise.

[Joy Christian]

In physical realizations these gates are realized by physical processes:
https://en.wikipedia.org/wiki/Quantum_c ... alizations
I assume you are not able to realize it with your model, but it would be great if you could show otherwise.

I cannot be bothered one way or the other. You wouldn't be asking me if you understood what I have stressed above. Please read all of my replies again. You might then get my message.

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[Jarek]

Indeed I read a very clear message, especially that it is really hard to imagine that you haven't tried simple quantum gates if believing to have a hidden variable model for more than a decade.
Don't worry, for this moment I believe a complete forward in time hidden variable model - covering also more complex situations, is just impossible - but would gladly change my mind.

[Joy Christian]

Indeed I read a very clear message, especially that it is really hard to imagine that you haven't tried simple quantum gates if believing to have a hidden variable model for more than a decade.
Don't worry, for this moment I believe a complete forward in time hidden variable model - covering also more complex situations, is just impossible - but would gladly change my mind.

Don't worry, I don't worry about your opinion at all. It is clear that you haven't got the message of my replies above. Unfortunately, my local-realistic model is not everyone's cup of tea.

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[Jarek]

I have just found that you have considered quantum computers: https://www.scottaaronson.com/blog/?p=993

As it is not that simple to verify, can maybe anybody else comment Joy's construction for Hardy's paradox?

[Joy Christian]

I have just found that you have considered quantum computers: https://www.scottaaronson.com/blog/?p=993

As it is not that simple to verify, can maybe anybody else comment Joy's construction for Hardy's paradox?

Ah.. so now you resort to a cheap shot by linking Aaronson. I have responded to Aaronson in a more dignified manner here: viewtopic.php?f=6&t=368#p8377

I have written up a long overdue refutation of Scott Aaronson's online critique of my local-realistic model:

Refutation of Scott Aaronson's Critique of my Disproof of Bell's Theorem

Fortunately, the Truth cannot be starved off so easily, and Aaronson has not succeeded in his goal.

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[Jarek]

I am just a blank page in this conflict, was looking for comments regarding your Hardy paradox construction, what has lead me to Scott's blog.
Anyway, I see you have considered quantum algorithms before and don't like them - I assume the reason is that your model didn't work for them, what is not very surprising as Shor's classical simulation would require retrocausality.
While current experimental realizations of Shor's algorithm are not extremely convincing, this algorithm is in agreement with QM - claiming it won't work would mean disagreeing with QM.

Ok, let's focus on Hardy's paradox in this thread. I don't believe it can be obtained by forward in time local hidden variable model, but pointing problem in your construction would require some work - I hope somebody else has already done it (?), otherwise I will probably look closer in some future.

[Joy Christian]

I am just a blank page in this conflict, was looking for comments regarding your Hardy paradox construction, what has lead me to Scott's blog.
Anyway, I see you have considered quantum algorithms before and don't like them - I assume the reason is that your model didn't work for them, what is not very surprising as Shor's classical simulation would require retrocausality.
While current experimental realizations of Shor's algorithm are not extremely convincing, this algorithm is in agreement with QM - claiming it won't work would mean disagreeing with QM.

Ok, let's focus on Hardy's paradox in this thread. I don't believe it can be obtained by forward in time local hidden variable model, but pointing problem in your construction would require some work - I hope somebody else has already done it (?), otherwise I will probably look closer in some future.

You are still not getting my message. I couldn't care less about Shor algorithm or any other algorithms. I don't need algorithms since they are irrelevant to the question of local realism.

As for my 3-sphere model, it reproduces all predictions of Hardy's state. It was considered and published by a Royal Society journal: https://royalsocietypublishing.org/doi/ ... sos.180526.

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[Jarek]

Shor "algorithm" is just an experimental setting - combination of multiple quantum operations.
Claiming a complete hidden variable model, you cannot just skip such physical settings.

Returning to Hardy, I see it wasn't included in your Royal Society paper.
Equation (91) in your https://arxiv.org/pdf/0904.4259.pdf says that expected value over the hidden variable is zero ... while in Hardy we have much stronger condition: for all hidden variables lambda, |11> is impossible.

[Joy Christian]

Shor "algorithm" is just an experimental setting - combination of multiple quantum operations.
Claiming a complete hidden variable model, you cannot just skip such physical settings.

Returning to Hardy, I see it wasn't included in your Royal Society paper.
Equation (91) in your https://arxiv.org/pdf/0904.4259.pdf says that expected value over the hidden variable is zero ... while in Hardy we have much stronger condition: for all hidden variables lambda, |11> is impossible.

I have not skipped any experimental settings. I don't care about any algorithms, Shor's or otherwise. What is important for local realism is that I have reproduced all predictions of quantum mechanics exactly, including those 16 predicted by the Hardy state. You are making claims about my model without actually reading my paper in detail, let alone understanding the model.

Lucien Hardy, by the way, is a friend of mine. We have known each other since before he got his Ph.D. He is well aware of my paper since it came out in 2009. The following footnote 3 on page 20 of my RSOS paper discusses the calculations within my model for the Hardy state. But you are right that explicit calculations of the Hardy state are not included in the RSOS paper because (among other things) the paper was getting far too long.



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[Jarek]

Functioning of Shor's algorithm is one of consequences of quantum mechanics - if you want to predict all, you also need this one.

Regarding Hardy, you write (91) is equivalent (61), but the latter says that probability is zero: it is forbidden for all lambda, while the former only says that average over lambda is zero.

[Heinera]

Lucien Hardy, by the way, is a friend of mine. We have known each other since before he got his Ph.D. He is well aware of my paper since it came out in 2009.
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Odd, then, that he has never publicly written a single word to defend your theory. But what do I know.