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    Uncertainty relations in terms of the Gini index for finite quantum systems

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    Publication date
    2020-04
    Author
    Vourdas, Apostolos
    Keyword
    Quantum systems
    Uncertainty relations
    Gini index
    Rights
    (c) 2020 IOP. Full-text reproduced in accordance with the publisher's self-archiving policy.
    Peer-Reviewed
    Yes
    
    Metadata
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    Abstract
    Lorenz values and the Gini index are popular quantities in Mathematical Economics, and are used here in the context of quantum systems with finite-dimensional Hilbert space. They quantify the uncertainty in the probability distribution related to an orthonormal basis. It is shown that Lorenz values are superadditive functions and the Gini indices are subadditive functions. The supremum over all density matrices of the sum of the two Gini indices with respect to position and momentum states is used to define an uncertainty coefficient which quantifies the uncertainty in the quantum system. It is shown that the uncertainty coefficient is positive, and an upper bound for it is given. Various examples demonstrate these ideas.
    URI
    http://hdl.handle.net/10454/17853
    Version
    Accepted manuscript
    Citation
    Vourdas A (2020) Uncertainty relations in terms of the Gini index for finite quantum systems. EPL (Europhysics Letters) 130(2): 20003.
    Link to publisher’s version
    https://doi.org/10.1209/0295-5075/130/20003
    Type
    Article
    Collections
    Engineering and Informatics Publications

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