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 accessAbstract
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].”
From Quantum Computing: Vision and Challenges (2025) · cites this paper as [74]
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Cites
Notes on black-hole evaporation
Unruh, W. G. (1976) · Physical Review D · doi:10.1103/physrevd.14.870 · Cited by 4,850
Scheme for reducing decoherence in quantum computer memory
Shor, P. W. (1995) · Physical Review A · doi:10.1103/physreva.52.r2493 · Cited by 4,479
Encyclopedia of Mathematics and its Applications.
L., Y. L., Jones, W. B., & Thron, W. J. (1982) · Mathematics of Computation · doi:10.2307/2007638 · Cited by 4,225
Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet
Holstein, T. D., & Primakoff, H. (1940) · Physical Review · doi:10.1103/physrev.58.1098 · Cited by 4,063
Generalized Coherent States and Their Applications
Perelomov, A. M. (1986) · Springer eBooks · doi:10.1007/978-3-642-61629-7 · Cited by 3,566
Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields
Hofstadter, D. R. (1976) · Physical Review B · doi:10.1103/physrevb.14.2239 · Cited by 3,495
Quantum Theory Of Angular Momemtum
Варшалович, Д. А., Moskalev, A. N., & Khersonskii, V. K. (1988) · Cited by 3,060
Foundations of Time-Frequency Analysis
Gröchenig, K. (2001) · Applied and numerical harmonic analysis · doi:10.1007/978-1-4612-0003-1 · Cited by 3,003
The Theory of Groups and Quantum Mechanics
Weyl, H. (1931) · International Linear Collider · Cited by 2,745
Error Correcting Codes in Quantum Theory
Steane, A. M. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.793 · Cited by 2,677
Research works printed but not linked: 14
- Schwinger J 1960 Proc. Natl Acad. Sci. USA 46 570
- McClellan J H and Parks T W 1972 IEEE Trans. Audio Electroacoust. 20 66
- Yarlagadda R 1977 IEEE Trans. Acoustics Speech Signal Proc. 25 586
- Dickinson B W and Steiglitz K 1982 IEEE Trans. Acoustics Speech Signal Proc. 30 25
- Klauder J R, Skagerstam B S 1985 Coherent States (Singapore: World Scientific)
- Walls D F and Milburn G 1994 Quantum Optics (Berlin: Springer)
- Kim Y S and Noz M E 1991 Phase Space Picture of Quantum Mechanics (Singapore: World Scientific)
- Lang S 1975 SL 2 (R) (Berlin: Springer)
- Moyal J E 1949 Proc. Cambridge Phil. Soc. 45 99
- Bartlett M S and Moyal J E 1949 Proc. Cambridge Phil. Soc. 45 545
- Nielsen M A and Chuang I L 2000 Quantum Information and Quantum Computing (Cambridge: Cambridge University Press)
- Rains E M 1999 IEEE Trans. Inf. Theo. 45 1827
- Asikhmin A and Knill E 2001 IEEE Trans. Inf. Theo. 47 3065 Vourdas A 2002 Phys. Rev. A 65 042321
- Berry M V 1987 Proc. R. Soc. A 473 183
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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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