Linear representations of probabilistic transformations induced by context transitions

Details Linear representations of probabilistic transformations induced by context transitions Linear representations of probabilistic transformations induced by context transitions

2001-05-13

arxiv.org/abs/quant-ph/0105059v2

J. of Physics,A: Math. and General, 34 (2001) 9965-9981

Physics

Quantum Physics

Added a physical discussion and new references

Scientific paper

10.1088/0305-4470/34/47/304

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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