Advances in Applied Clifford Algebras

, Volume 20, Issue 1, pp 43–56 | Cite as

Representation of Probabilistic Data by Quantum-Like Hyperbolic Amplitudes

  • Andrei Khrennikov


In this paper we study the problem of representation of statistical data of any origin by hyperbolic probabilistic amplitudes (normalized vectors in hyperbolic Hilbert space). It generalizes the conventional QM which is based on complex Hilbert space. We performed extended numerical simulation. Similar to the conventional quantum formalism for Bloch’s sphere, we visualize results of simulation for a special class of statistical data on so called Bloch’s hyperboloid. The notion of hyperbolic qubit is introduced.


Representation of probabilistic data by hyperbolic amplitudes Bloch’s sphere Bloch’s hyperboloid 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.International Center for Mathematical Modeling in Physics and Cognitive SciencesUniversity of VäxjöVäxjöSweden

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