Quantum Measurement Trees, I: Two Preliminary Examples of Induced Contextual Boolean Algebras

Peter J Hammond
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Peter J Hammond: University of Warwick

CRETA Online Discussion Paper Series from Centre for Research in Economic Theory and its Applications CRETA

Abstract: Quantum randomness evidently transcends the classical framework of random variables defined on a single comprehensive Kolmogorov probability space. One prominent example is the quantum double-slit experiment due to Feynman (1951, 1966). A related non-quantum example, inspired by Boole (1862) and Vorobev (1962), has three two-valued random variables X, Y and Z, where the pairs X; Y and X ; Z are perfectly correlated, yet Y ; Z are perfectly anti-correlated. Such examples can be accommodated using a "multi-measurable" space with several different algebras of measurable events. This concept due to Vorobev (1962) allows construction of : 1) a measurable metaspace whose elements combine a point in the original sample space with a variable "contextual" Boolean algebra ; 2) a parametric family of probability metaspaces, each of which is a Kolmogorov probability space that represents a two-stage stochastic process where a random choice from the original sample space is preceded by the random choice of a contextual Boolean algebra in the multi-measurable space. Subsequent work will explore how quantum experimental results can be described using a quantum measurement tree with one or more preparation nodes where an experimental configuration is determined that governs the probability distribution of relevant quantum observables.

Keywords: Quantum measurement tree; quantum challenge; double-slit; experiment; quantum contexts; multi-measurable space; measurable metaspace; multi-probability space; probability metaspace. (search for similar items in EconPapers)
Date: 2025
New Economics Papers: this item is included in nep-mac
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