CoChat
Sign Up
Cited by 321Quantum Mechanics and ApplicationsQuantum Information and CryptographyQuantum chaos and dynamical systems

The DOI matches its Crossref record; 156 of the 156 references it cites were found in a registry or an index.

Quantum systems with finite Hilbert space

Open access
Vourdas, A·2004·Reports on Progress in Physics
DOI 10.1088/0034-4885/67/3/r03
Open this paper in CoChat — free accountOpen PDF

Abstract

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.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1088/0034-4885/67/3/r03

Cites

156 of 156 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 156 references

Research works printed but not linked: 14

  1. Schwinger J 1960 Proc. Natl Acad. Sci. USA 46 570
  2. McClellan J H and Parks T W 1972 IEEE Trans. Audio Electroacoust. 20 66
  3. Yarlagadda R 1977 IEEE Trans. Acoustics Speech Signal Proc. 25 586
  4. Dickinson B W and Steiglitz K 1982 IEEE Trans. Acoustics Speech Signal Proc. 30 25
  5. Klauder J R, Skagerstam B S 1985 Coherent States (Singapore: World Scientific)
  6. Walls D F and Milburn G 1994 Quantum Optics (Berlin: Springer)
  7. Kim Y S and Noz M E 1991 Phase Space Picture of Quantum Mechanics (Singapore: World Scientific)
  8. Lang S 1975 SL 2 (R) (Berlin: Springer)
  9. Moyal J E 1949 Proc. Cambridge Phil. Soc. 45 99
  10. Bartlett M S and Moyal J E 1949 Proc. Cambridge Phil. Soc. 45 545
  11. Nielsen M A and Chuang I L 2000 Quantum Information and Quantum Computing (Cambridge: Cambridge University Press)
  12. Rains E M 1999 IEEE Trans. Inf. Theo. 45 1827
  13. Asikhmin A and Knill E 2001 IEEE Trans. Inf. Theo. 47 3065 Vourdas A 2002 Phys. Rev. A 65 042321
  14. Berry M V 1987 Proc. R. Soc. A 473 183

Cited by

Sorted by citations

Items 101–200 of 320

Related

See all

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
DOI
10.1088/0034-4885/67/3/r03
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
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

About these checks

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 ›

Are you an author, or do you see a problem with this page? Request a review