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    Lower and upper probabilities in the distributive lattice of subsystems

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    Publication date
    2014-08-12
    Author
    Vourdas, Apostolos
    Keyword
    Probabilities; Lower and upper probabilities; Distributive lattice; Subsystems; Quantum systems
    Rights
    © 2014 IOP Publishing. Reproduced in accordance with the publisher's self-archiving policy.
    Peer-Reviewed
    Yes
    
    Metadata
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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.
    URI
    http://hdl.handle.net/10454/7660
    Version
    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.
    Link to publisher’s version
    http://dx.doi.org/10.1088/1751-8113/47/34/345203
    Type
    Article
    Collections
    Engineering and Informatics Publications

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