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Non-additive probabilities and quantum logic in finite quantum systems

Publication Date
2016
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Keywords
Quantum logic; Quantum systems; Hilbert space; Kolmogorov probabilities
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Accepted for publication
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Engineering and Digital Technology Publications
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Abstract
A quantum system Σ(d) with variables in Z(d) and with Hilbert space H(d), is considered. It is shown that the additivity relation of Kolmogorov probabilities, is not valid in the Birkhoff-von Neumann orthocomplemented modular lattice of subspaces L(d). A second lattice Λ(d) which is distributive and contains the subsystems of Σ(d) is also considered. It is shown that in this case also, the additivity relation of Kolmogorov probabilities is not valid. This suggests that a more general (than Kolmogorov) probability theory is needed, and here we adopt the Dempster-Shafer probability theory. In both of these lattices, there are sublattices which are Boolean algebras, and within these 'islands' quantum probabilities are additive.
URI
http://hdl.handle.net/10454/11003
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Published version
Citation
Vourdas A (2016) Non-additive probabilities and quantum logic in finite quantum systems. Journal of Physics: Conference Series. 597. Conference 1.
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https://doi.org/10.1088/1742-6596/597/1/012073
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Conference paper
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