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I am reading device independent approach on quantum mechanics from here device independent outlook on quantum mechanics. In here the author introduces local variable theory. Then he give two results. First any local variable statistics can be explained by a deterministic local variable. Second some of the quantum statistics such as measurement in same basis on singlet state can be given by a deterministic local variable statistics. By statistics I mean there are two separate parties $A$ and $B$ with input sets being $x$ and $y$ respectively and output sets being $a$ and $b$ respectively. Also they share a pre-established agreement $\lambda$, and we are interested in $$P(a,b|x,y)=\int \rho(\lambda|x,y)P^{'}(a,b|x,y,\lambda)d\lambda$$ Sometimes the author says two theories give same statistics by comparing the expectations of results and sometimes he say two theories give same statistics if probability distribution for all cases is the same. Why is it so ?

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    $\begingroup$ Just a few remarks about quantum mysticism: within conventional quantum mechanics Bell inequalities are a tautology in the same sense that momentum and energy conservation are a tautology in classical mechanics: they are there because we put them there. From a mathematical point of view there is no point in trying to "derive" an axiom of a theory within the theory. Either the theory falls by a conclusive EXPERIMENT, or it doesn't. The paper itself looks like a collection of re-imagined facts and naive misunderstandings about QM. I would disregard it and look for something with substance. $\endgroup$ – CuriousOne May 26 '15 at 17:13
  • $\begingroup$ @CuriousOne I am just a beginner in quantum mechanics so I don't have a broad idea about it. But I feel disregard is a strong comment. I have come across a lot on bell polytopes. Even on the forum experienced users ask questions about it for example here physics.stackexchange.com/questions/8514/…. Keeping your point in my mind I will give it a try and see for myself whether the paper/topic is reasonable. $\endgroup$ – sashas May 26 '15 at 17:35
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    $\begingroup$ I am just trying to put these kinds of articles in the context of the definition of science for you. You can disregard it and chase this tail as long as you wish... eventually you will notice that a simple look at the definitions of "science" and "theory" would have lead you to the same conclusion that I just gave you. Einstein said it best: "We can not solve our problems with the same level of thinking that created them.", but that is exactly what quantum mysticism is trying to do. $\endgroup$ – CuriousOne May 26 '15 at 17:40
  • $\begingroup$ @CuriousOne: I have to disagree. From what I know about the buzzwords in the abstract, what people are really trying to do is twofold: First, they consider theories that are NOT quantum mechanics but seem to also describe at least some quantum experiments and try to argue that these theories are not worth pursuing - one way to do that is to prove that the Bell inequalities are different. You can argue that this was to be expected and I would agree that a lot of the "Foundations of Quantum Mechanics" is rather weird mysticism, but it is not completely without substance. $\endgroup$ – Martin May 27 '15 at 9:54
  • $\begingroup$ Second, this is about "device independent tests". Such things are usually rather uninteresting from a scientific perspective, but they are very intersting from a cryptographic/engineering perspective: Given a box that tells you it outputs two maximally entangled states, how can you be sure that it actually does this? Maximal violation of a Bell inequality in my own lab would be one naive way. $\endgroup$ – Martin May 27 '15 at 9:55

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