Jarek Duda

Welcome to Wikimedia Commons, Jarek Duda!

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-- Wikimedia Commons Welcome (talk) 05:22, 5 September 2016 (UTC)

Hey Jarek, I think the example image for ANS encoding has a small error? I made a note on the discussion page. (Thanks for ANS!) - Dominic P. Cooney (talk) 01:16, 20 June 2018 (UTC)

Thank you for reporting - I have just corrected it (and mentioned you in file changes). --Jarek Duda (talk) 07:44, 20 June 2018 (UTC)

Bell's inequality

Dear Jarek, I got interested in your illustration https://commons.m.wikimedia.org/wiki/File:Bell_theorem.png . Could you please clarify what is the state space and how the observables ABC are related there? Thank you. L3erdnik (talk) 23:12, 6 March 2020 (UTC)

Dear L3erdnik, derivation is universal for 3 binary variables ABC. I wanted to find a simplest way to violate this inequality, and finally used mathematical similarity between Feynman and Boltzmann path ensembles - while the former is equivalent with QM, the latter is realized e.g. in Ising model: https://physics.stackexchange.com/questions/524856/violation-of-bell-like-inequalities-with-spatial-boltzmann-path-ensemble-ising Jarek Duda (talk) 05:59, 7 March 2020 (UTC)

Thank you for the link, but it seems the physics there is a bit beyond the standard QM, so could you please translate to me, what are the observables and the state coordinate wise (explicitly in some basis)? Sorry for bothering you, it is just for a moment I thought it was just a different phrasing of Mermin inequality, but it has 3/4, not .6 for the sum, so I'm confused. L3erdnik (talk) 15:02, 7 March 2020 (UTC)

This is standard Ising model - Boltzmann distribution among possible sequences. It has similar mathematics as QM in Feynman path ensembles, but leads to a bit different maximal violation, e.g. 3/4 vs 3/5 for Mermin. We have 3 binary variables (|Omega|=8), and measure only two of them at once. If prepared state would be defined by probability distribution on Omega, then inequality would have to be satisfied. It is crucial that in Feynman/Boltzmann path ensembles we define state by amplitude on Omega - to be added for unmeasured variables, then multiplied. In Boltzmann case (real nonnegative psi), state maximizing violation is psi000=psi111=0, psi001=psi010=psi100=psi011=psi101=psi110=1/sqrt(6).Jarek Duda (talk) 15:20, 7 March 2020 (UTC)

Sorry, I still don't get it. Btw, we can switch to email if you'd like. Are you saying that this is a model incompatible with QM (since it predicts different probabilities)? Also, I know Ising model as "2 possible states for each particle per each node", not "1 particle with a state per node" which it seems like in your example. Also I can't shake off the impression that your variables ABC are independent (ie can be measured all at once), in which case there should be no violation of Bell's inequality. I haven't found any literature that defines "Boltzmann's path ensemble for Ising model" (I only know the usual Boltzmann's ensemble for states with different energies), so that might clear up things for me... L3erdnik (talk) 20:34, 7 March 2020 (UTC)

Ising model is different from QM, but they use similar mathematics: the former uses Boltzmann sequence ensemble, the latter uses Feynman path ensemble. We can use this mathematical similarity to translate Bell violation mechanism between them. My construction uses e.g. "3 x infinity" Ising model: 1D sequence of 3 spins (8 possibilities). Think about probability distribution inside such general Ising model - the lower diagram in above stackexchange link has sketch of derivation. Measurement of AB means that we ask about their values, and erase information about the remaining C - to add its amplitudes before squaring in Born rule. (slide 5 sketch of derivation, 22 Bell in https://www.dropbox.com/s/m1m8uq0gygo2lzt/Ising.pdf ) Jarek Duda (talk) 21:16, 7 March 2020 (UTC)