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.
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/7660 |
| Date | 07 July 2014 |
| Creators | Vourdas, Apostolos |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Article, Accepted Manuscript |
| Rights | © 2014 IOP Publishing. Reproduced in accordance with the publisher's self-archiving policy. |
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