Lower and upper probabilities in the distributive lattice of subsystems
dc.contributor.author | Vourdas, Apostolos | * |
dc.date.accessioned | 2016-01-11T14:29:00Z | |
dc.date.available | 2016-01-11T14:29:00Z | |
dc.date.issued | 2014-08-12 | |
dc.identifier.citation | Vourdas A (2014) Lower and upper probabilities in the distributive lattice of subsystems. Journal of Physics A: Mathematical and Theoretical. 47(34): 345203. | en_US |
dc.identifier.uri | http://hdl.handle.net/10454/7660 | |
dc.description | yes | en_US |
dc.description.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. | |
dc.language.iso | en | en_US |
dc.rights | © 2014 IOP Publishing. Reproduced in accordance with the publisher's self-archiving policy. | en_US |
dc.subject | Probabilities; Lower and upper probabilities; Distributive lattice; Subsystems; Quantum systems | en_US |
dc.title | Lower and upper probabilities in the distributive lattice of subsystems | en_US |
dc.status.refereed | Yes | en_US |
dc.type | Article | en_US |
dc.type.version | Accepted Manuscript | en_US |
dc.identifier.doi | https://doi.org/10.1088/1751-8113/47/34/345203 | |
refterms.dateFOA | 2018-07-25T13:21:13Z | |
dc.date.accepted | 2014-07-07 |