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Unitarily inequivalent local and global Fourier transforms in multipartite quantum systems
Lei, Ci
Lei, Ci
Publication Date
2023-01
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© 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
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Open Access status
openAccess
Accepted for publication
2022-12-28
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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.
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.
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Article