by **Jarek** » Sat Sep 09, 2017 1:04 am

Why do you think it is different from having 3 coins: 8 possibilities (000,001,010,011,100,101,110,111) with some probability distribution among them (P(ABC)) ?

Measuring two of them, there is still some probability distribution for the third one: P(AB) = P(AB0) + P(AB1).

The above assumption implies e.g. P(A=B) + P(B=C) + P(A=C) >=1, violated e.g. in QM.

Indeed the problem is to pin down the issue with the above "3 coin" picture with some hidden probability distribution P(ABC).

The crucial hint is the quantum measurement process, which is quite invasive/destructive, e.g. like its idealization: Stern-Gerlach experiment, taking continuous space of initial spin directions, and enforcing final discrete: parallel or anti-parallel alignment to the strong magnetic field.

This way "measuring 2 coins", we somehow influence the third one - leading to Bell violation.

But understanding the details is far from trivial - we need a simple model with some resemblance to QM, like Born rules - also leading to Bell violation.

And MERW fits perfectly here - it is just uniform probability distribution among paths on a graph, allowing to derive Born rules in just 2 lines:

https://en.wikipedia.org/wiki/Maximal_E ... derivationSpecifically, we ask for the number of length 2L paths with vertex i in the center (sum_{jk} (A^L)_{ji} (A^L)_{ik}), which in the L -> infinity limit gives Born rule: Pr(i) ~ psi_i^2, where psi turns out exactly the quantum ground state amplitude.

... and such Born rules lead to violation of Bell inequalities:

https://www.dropbox.com/s/ax35hvxrorx72ff/bell_MERW.pdf
Why do you think it is different from having 3 coins: 8 possibilities (000,001,010,011,100,101,110,111) with some probability distribution among them (P(ABC)) ?

Measuring two of them, there is still some probability distribution for the third one: P(AB) = P(AB0) + P(AB1).

The above assumption implies e.g. P(A=B) + P(B=C) + P(A=C) >=1, violated e.g. in QM.

Indeed the problem is to pin down the issue with the above "3 coin" picture with some hidden probability distribution P(ABC).

The crucial hint is the quantum measurement process, which is quite invasive/destructive, e.g. like its idealization: Stern-Gerlach experiment, taking continuous space of initial spin directions, and enforcing final discrete: parallel or anti-parallel alignment to the strong magnetic field.

This way "measuring 2 coins", we somehow influence the third one - leading to Bell violation.

But understanding the details is far from trivial - we need a simple model with some resemblance to QM, like Born rules - also leading to Bell violation.

And MERW fits perfectly here - it is just uniform probability distribution among paths on a graph, allowing to derive Born rules in just 2 lines: https://en.wikipedia.org/wiki/Maximal_Entropy_Random_Walk#Sketch_of_derivation

Specifically, we ask for the number of length 2L paths with vertex i in the center (sum_{jk} (A^L)_{ji} (A^L)_{ik}), which in the L -> infinity limit gives Born rule: Pr(i) ~ psi_i^2, where psi turns out exactly the quantum ground state amplitude.

... and such Born rules lead to violation of Bell inequalities: https://www.dropbox.com/s/ax35hvxrorx72ff/bell_MERW.pdf