Abstract
Representation of an abstract quantum logic withan ordering set of states S in the form of a family L(S) of fuzzy subsets of S which fulfils conditionsanalogous to Kolmogorovian conditions imposed on σ-algebra of random events allows us toconstruct quantum probability calculus in a waycompletely parallel to the classical Kolmogorovianprobability calculus. It is shown that the quantumprobability calculus so constructed is a propergeneralization of the classical Kolmogorovian one. Someindications for building a phase-space representation ofquantum mechanics free of the problem of negativeprobabilities are given.
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Pykacz, J. Fuzzy Quantum Logics as a Basis for Quantum Probability Theory. International Journal of Theoretical Physics 37, 281–290 (1998). https://doi.org/10.1023/A:1026618818509
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DOI: https://doi.org/10.1023/A:1026618818509