Two examples in noncommutative probability

Andrei Yu. Khrennikov, Sergei Vladimirovich Kozyrev

Anilesh Mohari

Andrei Yu. Khrennikov

In this chapter we consider two examples of the situation when the classicalobservables should be described by a noncommutative (quantum-like)probability space. A possible experimental approach to find quantum-like correlationsfor classical disordered systems is discussed. The interpretation ofnoncommutative probability in experiments with classical systems as a resultof context (complex of experimental physical conditions) dependence ofprobability is considered.

Jean-Paul Marchand

Naofumi Muraki

The monotone Fock space was introduced by the author to construct a new example of noncommutative “de Moivre Laplace theorem ” [1] and of noncommutative “Brow-nian motion ” [2] in quantum probability theory (see [3] [4] for general reference to quantum probability). We note that the essentially same structure was introduced

Andrey Anatoljevich Grib, Andrei Yu. Khrennikov, K Starkov

Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude are given. The first game is described by the quantum formalism of spin one half system for which two noncommuting observables are measured. The second game corresponds to the spin one case. Quantum logical orthocomplemented nondistributive lattices for these two games are presented. Interference terms for the probability amplitudes are analyzed by using so called contextual approach to probability (in the von Mises frequency approach). We underline that our games are not based on using of some microscopic systems. The whole scenario is macroscopic.