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Lower and upper probabilities in the distributive lattice of subsystems
Publication Date
2014-08-12
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© 2014 IOP Publishing. Reproduced in accordance with the publisher's self-archiving policy.
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2014-07-07
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Abstract
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.
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Accepted Manuscript
Citation
Vourdas A (2014) Lower and upper probabilities in the distributive lattice of subsystems. Journal of Physics A: Mathematical and Theoretical. 47(34): 345203.
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Article