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Quantum systems with finite Hilbert space
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Quantum systems with finite Hilbert space are considered, and phase-space methods like the Heisenberg–Weyl group, symplectic transformations and Wigner and Weyl functions are discussed. A factorization of such systems in terms of smaller subsystems, based on the Chinese remainder theorem, is studied. The general formalism is applied to the case of angular momentum. In this context, SU (2) coherent states are used for analytic representations. Links between the theory of finite quantum systems and other fields of research are discussed.
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“When developing quantum computers, simulators can make use of entanglement and superposition, two of their key features [74].”
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Metadata
- Authors
- Vourdas, A.
- Affiliations
- University of Bradford (GB)
- Corresponding author
- Vourdas, A
- ORCID
- Vourdas, A
- Venue
- Reports on Progress in Physics
- Publisher
- IOP Publishing
- Published
- 2004-02-02
- Volume
- 67
- Issue
- 3
- Pages
- 267-320
- ISSN
- 0034-4885 (ISSN-L)
- 1361-6633
- OpenAlex
- W2058124214
- Cited by
- 321
- References
- 156
- Citations by year
- 2026: 10 · 2025: 18 · 2024: 13 · 2023: 8 · 2022: 14 · 2021: 14 · 2020: 9 · 2019: 9 · 2018: 10 · 2017: 12 · 2016: 22 · 2015: 12 · 2014: 18 · 2013: 19 · 2012: 14
- FWCI
- 12.07
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Reports on Progress in Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Keywords
- finite-dimensional quantum systems, finite-dimensional Hilbert space, Weyl-Heisenberg group, symplectic transformations, Wigner function, Weyl function, Chinese remainder theorem, angular momentum, SU(2) coherent states, analytic signal
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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