dorsal/arxiv
View SchemaLinear representations of probabilistic transformations induced by context transitions
| Authors | Andrei Khrennikov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0105059 |
| URL | https://arxiv.org/abs/quant-ph/0105059 |
| DOI | 10.1088/0305-4470/34/47/304 |
| Journal | J. of Physics,A: Math. and General, 34 (2001) 9965-9981 |
Abstract
By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to statistical deviations of different magnitudes: (a) trigonometric; (b) hyperbolic; (c) hyper-trigonometric. It is shown that not only quantum preparation procedures can have trigonometric probabilistic behaviour. We propose generalizations of ${\bf C}$-linear space probabilistic calculus to describe non quantum (trigonometric and hyperbolic) probabilistic transformations. We also analyse superposition principle in this framework.
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"abstract": "By using straightforward frequency arguments we classify transformations of\nprobabilities which can be generated by transition from one preparation\nprocedure (context) to another. There are three classes of transformations\ncorresponding to statistical deviations of different magnitudes: (a)\ntrigonometric; (b) hyperbolic; (c) hyper-trigonometric. It is shown that not\nonly quantum preparation procedures can have trigonometric probabilistic\nbehaviour. We propose generalizations of ${\\bf C}$-linear space probabilistic\ncalculus to describe non quantum (trigonometric and hyperbolic) probabilistic\ntransformations. We also analyse superposition principle in this framework.",
"arxiv_id": "quant-ph/0105059",
"authors": [
"Andrei Khrennikov"
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"quant-ph"
],
"doi": "10.1088/0305-4470/34/47/304",
"journal_ref": "J. of Physics,A: Math. and General, 34 (2001) 9965-9981",
"title": "Linear representations of probabilistic transformations induced by context transitions",
"url": "https://arxiv.org/abs/quant-ph/0105059"
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