dorsal/arxiv
View SchemaOn generalized probabilities: correlation polytopes for automaton logic and generalized urn models, extensions of quantum mechanics and parameter cheats
| Authors | Karl Svozil |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0012066 |
| URL | https://arxiv.org/abs/quant-ph/0012066 |
Abstract
Three extensions and reinterpretations of nonclassical probabilities are reviewed. (i) We propose to generalize the probability axiom of quantum mechanics to self-adjoint positive operators of trace one. Furthermore, we discuss the Cartesian and polar decomposition of arbitrary normal operators and the possibility to operationalize the corresponding observables. Thereby we review and emphasize the use of observables which maximally represent the context. (ii) In the second part, we discuss Pitowsky polytopes for automaton logic as well as for generalized urn models and evaluate methods to find the resulting Boole-Bell type (in)equalities. (iii) Finally, so-called ``parameter cheats'' are introduced, whereby parameters are transformed bijectively and nonlinearly in such a way that classical systems mimic quantum correlations and vice versa. It is even possible to introduce parameter cheats which violate the Boole-Bell type inequalities stronger than quantum ones, thereby trespassing the Tsirelson limit. The price to be paid is nonuniformity.
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"abstract": "Three extensions and reinterpretations of nonclassical probabilities are\nreviewed. (i) We propose to generalize the probability axiom of quantum\nmechanics to self-adjoint positive operators of trace one. Furthermore, we\ndiscuss the Cartesian and polar decomposition of arbitrary normal operators and\nthe possibility to operationalize the corresponding observables. Thereby we\nreview and emphasize the use of observables which maximally represent the\ncontext. (ii) In the second part, we discuss Pitowsky polytopes for automaton\nlogic as well as for generalized urn models and evaluate methods to find the\nresulting Boole-Bell type (in)equalities. (iii) Finally, so-called ``parameter\ncheats\u0027\u0027 are introduced, whereby parameters are transformed bijectively and\nnonlinearly in such a way that classical systems mimic quantum correlations and\nvice versa. It is even possible to introduce parameter cheats which violate the\nBoole-Bell type inequalities stronger than quantum ones, thereby trespassing\nthe Tsirelson limit. The price to be paid is nonuniformity.",
"arxiv_id": "quant-ph/0012066",
"authors": [
"Karl Svozil"
],
"categories": [
"quant-ph"
],
"title": "On generalized probabilities: correlation polytopes for automaton logic and generalized urn models, extensions of quantum mechanics and parameter cheats",
"url": "https://arxiv.org/abs/quant-ph/0012066"
},
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