Quantum Measurement Trees, I: Two Preliminary Examples of Induced Contextual Boolean Algebras
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916972346736640 |
|---|---|
| author | Hammond, Peter J |
| author_facet | Hammond, Peter J |
| contents | 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$-algebras of measurable events. This concept due to Vorob$'$ev (1962) allows construction of: 1) a measurable meta\-space whose elements combine a point in the original sample space with a variable ``contextual'' Boolean algebra; 2) a parametric family of probability meta\-spaces, each of which is a Kolmogorov probability space that represents a two-stage stochastic process where a random choice from the original sample space is preceded by the random choice of a contextual Boolean algebra in the multi-measurable space. Subsequent work will explore how quantum experimental results can be described using a quantum measurement tree with one or more preparation nodes where an experimental configuration is determined that governs the probability distribution of relevant quantum observables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Measurement Trees, I: Two Preliminary Examples of Induced Contextual Boolean Algebras Hammond, Peter J Quantum Physics Quantum Theory 81 (Primary) 81P13 (Secondary), Probability Theory 60 (Primary) 60A05 (Secondary) Quantum randomness evidently transcends the classical framework of random variables defined on a single comprehensive Kolmogorov probability space. One prominent example is the quantum double-slit experiment due to Feynman (1951, 1966). A related non-quantum example, inspired by Boole (1862) and Vorob$'$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. |
| title | Quantum Measurement Trees, I: Two Preliminary Examples of Induced Contextual Boolean Algebras |
| topic | Quantum Physics Quantum Theory 81 (Primary) 81P13 (Secondary), Probability Theory 60 (Primary) 60A05 (Secondary) |
| url | https://arxiv.org/abs/2509.22594 |