dorsal/arxiv
View SchemaLess (precision) is more (information): quantum information in fuzzy probability theory
| Authors | Paul Busch |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0401027 |
| URL | https://arxiv.org/abs/quant-ph/0401027 |
| Journal | Proceedings, A Khrennikov (ed.), Vaxjo University Press, pp. 113-128 (2004), ISBN: 978-9176364093 |
Abstract
A comparison of structural features of quantum and classical physical theories, such as the information capacity of systems subject to these theories, requires a common formal framework for the presentation of corresponding concepts (such as states, observables, probability, entropy). Such a framework is provided by the notion of statistical model developed in the convexity approach to statistical physical theories. Here we use statistical models to classify and survey all possible types of embedding and extension of quantum probabilistic theories subject to certain reasonable constraints. It will be shown that the so-called canonical classical extension of quantum mechanics is essentially the only `good' representation of the quantum statistical model in a classical framework. All quantum observables are thus identified as fuzzy classical random variables.
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"abstract": "A comparison of structural features of quantum and classical physical\ntheories, such as the information capacity of systems subject to these\ntheories, requires a common formal framework for the presentation of\ncorresponding concepts (such as states, observables, probability, entropy).\nSuch a framework is provided by the notion of statistical model developed in\nthe convexity approach to statistical physical theories. Here we use\nstatistical models to classify and survey all possible types of embedding and\nextension of quantum probabilistic theories subject to certain reasonable\nconstraints. It will be shown that the so-called canonical classical extension\nof quantum mechanics is essentially the only `good\u0027 representation of the\nquantum statistical model in a classical framework. All quantum observables are\nthus identified as fuzzy classical random variables.",
"arxiv_id": "quant-ph/0401027",
"authors": [
"Paul Busch"
],
"categories": [
"quant-ph"
],
"journal_ref": "Proceedings, A Khrennikov (ed.), Vaxjo University Press, pp.\n 113-128 (2004), ISBN: 978-9176364093",
"title": "Less (precision) is more (information): quantum information in fuzzy probability theory",
"url": "https://arxiv.org/abs/quant-ph/0401027"
},
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