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Lower and upper probabilities in the distributive lattice of subsystems

yes / The set of subsystems ∑ (m) of a finite quantum system ∑(n) (with variables in Ζ(n)) together with logical connectives, is a distributive lattice. With regard to this lattice, the ℓ(m | ρn) = Tr (𝔓(m) ρn ) (where 𝔓(m) is the projector to ∑(m)) obeys a supermodularity inequality, and it is interpreted as a lower probability in the sense of the Dempster–Shafer theory, and not as a Kolmogorov probability. It is shown that the basic concepts of the Dempster–Shafer theory (lower and upper probabilities and the Dempster multivaluedness) are pertinent to the quantum formalism of finite systems.

Identiferoai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/7660
Date07 July 2014
CreatorsVourdas, Apostolos
Source SetsBradford Scholars
LanguageEnglish
Detected LanguageEnglish
TypeArticle, Accepted Manuscript
Rights© 2014 IOP Publishing. Reproduced in accordance with the publisher's self-archiving policy.

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