Bananaworld: Quantum Mechanics for Primates

TL;DR

This paper explores quantum mechanics as a theory of probabilistic correlations and information structure, illustrating how nonclassical correlations defy classical explanation using a banana analogy.

Contribution

It presents a novel perspective that quantum correlations can be understood as probabilistic correlations of information, using a playful banana analogy to clarify complex concepts.

Findings

Quantum correlations lie outside the local correlation polytope.

Nonclassical features include irreducible information loss on measurement.

Quantum correlations cannot be explained by classical theories without abandoning fundamental principles.

Abstract

This is intended to be a serious paper, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, since a theory of information is essentially a theory of probabilistic correlations. To make this clear, it suffices to consider measurements of two binary-valued observables, x with outcomes a = 0 or 1, performed by Alice in a region A, and y with outcomes b = 0 or 1 performed by Bob in a separated region B --or, to emphasize the banality of the phenomena, two ways of peeling a banana, resulting in one of two tastes. The imagined bananas of Bananaworld are non-standard, with operational or phenomenal probabilistic correlations for peelings and tastes that lie outside the polytope of local correlations. The 'no go' theorems tell us that we can't shoe-horn these correlations into a classical correlation polytope, which has the structure of a simplex, by supposing that something has been left out of the story, without giving up fundamental principles that define what we mean by a physical system. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are shown to be generic features of correlations that lie outside the local correlation polytope. As far as the conceptual problems are concerned, we might as well talk about bananas.