2025/09/26 by Peter J. Hammond, Hammond, Peter J · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Probability Theory 60 (Primary) 60A05 (Secondary) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum Theory 81 (Primary) 81P13 (Secondary)
paper · pdf · doi:10.48550/arxiv.2509.22594
openalex publication_date 2025/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Vorob'ev (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 σ-algebras of measurable events. This concept due to Vorob'ev (1962) allows construction of: 1) a measurable meta\-space whose elements combine a point in the original sample space with a variable ``contextual'' Boolean algebra; 2) a parametric family of probability meta\-spaces, 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.