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Hi, author of the article here. Regarding determinism, I think the reason the assertion is "no deterministic local hidden.." is that, you need to break both th
by Maro 2y ago
Hi, author of the article here.
Regarding determinism, I think the reason the assertion is "no deterministic local hidden.." is that, you need to break both the deterministic and locality assumption. However there is a nuance, which is, do you need to break both properties to..
(a) break the Bell inequalities, or, to
(b) reproduce quantum mechanics..
which is not exactly the same thing.
For example, in my toy simulation framework, this [1] simple setup --- where Alice's two measurement devices always return +1, and Bob's two measurement devices are conditioned on Alice's returned value, without any randomness --- breaks the Bell-inequalities at S=4, but:
(1) it's not physical, because it also breaks the Tsirelson bound (4 > 2.82), ie. you can't actually achieve this with any known real-world physical system
(2) it's deterministic in the sense that the code does not call `random()`
(3) but from the perspective of Bob, who "calls" the measurement function, it would still appear random, since it depends on whether Alice measures H or T, which was the outcome of a random coin flip; so whether we consider this random is quite nuanced..
So the above is an interesting thought/Python experiment for what it takes to break the Bell inequalities. Then, if we modify the code to reproduce quantum mechanics (for which the 2 qubits stand in), which is the code shown in the original post, in that case we cannot even avoid calling `random()`, because the "first" to measure their qubit must also get +1 and -1 with equal probabilility, so the theory cannot be deterministic.
[1] https://gist.github.com/mtrencseni/de13f766911aaaf5bfd5d4636c109dbb https://gist.github.com/mtrencseni/de13f766911aaaf5bfd5d4636...
- n4r9 2y agoYes I could have worded that better! So... what you have here is a deterministic non-local hidden variable model which violates Bell Inequalities. The reduced probabilities at Bob's end might look random to him, but fundamentally the measurement outcomes are determined by Alice and Bob's measurement choices. All good. You also know that any deterministic local hidden variable model must obey Bell Inequalities. What I'm saying is that any local hidden variable model must obey Bell Inequalities. You cannot increase the value of S by relaxing determinism. So actually it's kind of a distraction to bring in determinism. Either you have local hidden variables - which obey Bell Inequalities - or you allow non-local hidden variables - in which case Bell Inequalities can be violated. Locality is the key assumption.
- n4r9 2y agoA follow-up point: it sounds like you're also wondering whether it's possible to simulate quantum mechnics exactly with a deterministic non-local hidden variable model? Arguably, this is exactly what the Bohmian "Pilot-wave" interpretation of quantum mechanics is - see e.g. https://plato.stanford.edu/entries/qm-bohm/ https://plato.stanford.edu/entries/qm-bohm/
- Maro 2y agoThanks for the pointer. To be honest, I wasn't wondering that :) From what I understand, historically nothing ever came of these different interpretations of QM. I subscribe to the Feynman motto of "shut up and calculate", with the modern modification of ".. or simulate".