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.
“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]
Section 14.2 identifies quantum computing as an application of finite quantum systems, and the Introduction links those systems to entanglement. The paper does not say that simulators used to develop quantum computers make use of entanglement and superposition; a search for simulators did not establish that part of the claim. No page numbers were available in our copy. (LLM, conf=0.76)
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Mann, A., Revzen, M., & Žák, J. (2005) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/38/21/l03 · Cited by 15 · see citing works
ABOUT THE MEAN KING'S PROBLEM AND DISCRETE WIGNER DISTRIBUTIONS
Durt, T. (2006) · International Journal of Modern Physics B · doi:10.1142/s0217979206034261 · Cited by 15 · see citing works
Maximal entanglement, collective coordinates and tracking the King
Revzen, M. (2013) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/46/7/075303 · Cited by 14 · see citing works
GALOIS FIELD QUANTUM MECHANICS
Chang, L. N., Lewis, Z., Minić, D., & Takeuchi, T. (2013) · Modern Physics Letters B · doi:10.1142/s0217984913500644 · Cited by 14 · see citing works
Quantum Fourier transform, Heisenberg groups and quasi-probability distributions
Patra, M. K., & Braunstein, S. L. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/6/063013 · Cited by 14 · see citing works
Harmonic Analysis on a Galois Field and Its Subfields
Vourdas, A. (2008) · Journal of Fourier Analysis and Applications · doi:10.1007/s00041-007-9000-2 · Cited by 14 · see citing works
Self-citationA complementarity-based approach to phase in finite-dimensional quantum systems
Klimov, A. B., Sánchez-Soto, L. L., & de Guise, H. (2005) · Journal of Optics B Quantum and Semiclassical Optics · doi:10.1088/1464-4266/7/9/008 · Cited by 14 · see citing works
- 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 › Computer Science › Artificial Intelligence › 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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