Jarek wrote: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?
Jarek wrote:Quantum algorithms, especially Shor, are the ultimate test.
Jarek wrote: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 ...
Jarek wrote:If you cannot, then your hidden variable is still missing something - might handle simple cases, but does not generalize.
Jarek wrote: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?
Jarek wrote: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.
Jarek wrote: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.
Jarek wrote: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.
Jarek wrote: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 wrote:Joy Christian wrote:
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 wrote: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.
Jarek wrote: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 wrote: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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