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BananaworldQuantum Mechanics for Primates$
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Jeffrey Bub

Print publication date: 2016

Print ISBN-13: 9780198718536

Published to Oxford Scholarship Online: March 2016

DOI: 10.1093/acprof:oso/9780198718536.001.0001

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The Big Picture

The Big Picture

(p.106) 5 The Big Picture

Jeffrey Bub

Oxford University Press

Correlations satisfying the no-signaling principle (“no information should be available to Alice in region A about alternative choices made by Bob in region B”) can be represented by three nested sets. The innermost set (a polytope, or multidimensional polygon) represents probabilistic correlations for which something has been left out of the story: the common causes or “hidden variables” that explain how the correlations arise. A simulation with local resources corresponds to a common cause explanation. Correlations in Bananaworld represented by points inside this set are completely explained by the bananas having what Einstein called a “being-thus,” an independent existence characterized by definite properties, prior to any peeling, associated with a particular taste for a particular peeling. The outermost set (also a polytope) represents all the probabilistic correlations between tastes and peelings for a pair of bananas that satisfy the no-signaling principle. Quantum correlations are represented by a set with a continuous boundary between the two polytopes.

Keywords:   local correlation polytope, no-signaling polytope, local simulation, common cause explanation, common cause, hidden variable, being-thus

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