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    Unitarily inequivalent local and global Fourier transforms in multipartite quantum systems

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    Publication date
    2023-01
    Author
    Lei, Ci
    Vourdas, Apostolos
    Keyword
    Finite quantum systems
    Local and global Fourier transforms
    Multipartite systems
    Rights
    © 2023 Springer. Reproduced in accordance with the publisher's self-archiving policy. The final publication is available at Springer via https://doi.org/10.1007/s11128-022-03820-2
    Peer-Reviewed
    Yes
    Open Access status
    openAccess
    
    Metadata
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    Abstract
    A multipartite system comprised of n subsystems, each of which is described with ‘local variables’ in Z(d) and with a d-dimensional Hilbert space H(d), is considered. Local Fourier transforms in each subsystem are defined and related phase space methods are discussed (displacement operators, Wigner and Weyl functions, etc). A holistic view of the same system might be more appropriate in the case of strong interactions, which uses ‘global variables’ in Z(dn) and a dn-dimensional Hilbert space H(dn). A global Fourier transform is then defined and related phase space methods are discussed. The local formalism is compared and contrasted with the global formalism. Depending on the values of d, n the local Fourier transform is unitarily inequivalent or unitarily equivalent to the global Fourier transform. Time evolution of the system in terms of both local and global variables, is discussed. The formalism can be useful in the general area of Fast Fourier transforms.
    URI
    http://hdl.handle.net/10454/19316
    Version
    Published version
    Citation
    Lei C and Vourdas A (2023) Unitarily inequivalent local and global Fourier transforms in multipartite quantum systems. Quantum Information Processing. 22(1): 78.
    Link to publisher’s version
    https://doi.org/10.1007/s11128-022-03820-2
    Type
    Article
    Collections
    Engineering and Informatics Publications

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