Re: Simple violation of Bell inequalities
Posted: Wed Jun 05, 2019 12:55 am
For completeness, I have added CHSH inequality - taking a million of random amplitudes, in ~0.5% of cases there is exceeded 2 value, what is impossible classically.
Mathematica file: https://www.dropbox.com/s/a0n0kb8cqazgz2j/CHSH.nb
This is for MERW ( https://en.wikipedia.org/wiki/Maximal_E ... andom_Walk ): assuming uniform (or Boltzmann) distribution among paths, what can be seen as QM in imaginary time.
It has Born rule: pr ~ psi^2, where one psi comes from ensemble of past paths, the other from future (this is time symmetric model).
To violate Bell-like inequalities (derived without such square), we need to design situations where we first add amplitudes of unmeasured variables, then perform the square.
Here is such construction for P(A=B) + P(B=C) + P(A=C) >=1 from page 9 of updated https://arxiv.org/pdf/0910.2724
Mathematica file: https://www.dropbox.com/s/a0n0kb8cqazgz2j/CHSH.nb
This is for MERW ( https://en.wikipedia.org/wiki/Maximal_E ... andom_Walk ): assuming uniform (or Boltzmann) distribution among paths, what can be seen as QM in imaginary time.
It has Born rule: pr ~ psi^2, where one psi comes from ensemble of past paths, the other from future (this is time symmetric model).
To violate Bell-like inequalities (derived without such square), we need to design situations where we first add amplitudes of unmeasured variables, then perform the square.
Here is such construction for P(A=B) + P(B=C) + P(A=C) >=1 from page 9 of updated https://arxiv.org/pdf/0910.2724