Entangled quantum systems and the Schmidt decomposition
Abstract
Quantum systems comprised of interacting subsystems become highly correlated and their individual identities become entangled. This entanglement can be described using the Schmidt decomposition, in which a pair of preferred orthonormal bases can be constructed to emphasize the tight correlations between two quantum subsystems. Examples are given of how the Schmidt basis can be exploited to shed new light on entangled subsystems in quantum optics, paying special attention to two-mode squeezed states and to atom–field interaction.
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The trace of the squared reduced density matrix ρ_r^2 determines purity of the reduced state and coincides with the inverse Schmidt entanglement parameter K^{-1}.
“As is known [14,15], the trace of the squared reduced density matrix ρ 2 r determines purity of the reduced state coinciding with the inverse value of the Schmidt entanglement parameter K -1 .”
From Entanglement of biphoton states: qutrits and ququarts (2011) · cites this paper as [15]
According to the Schmidt decomposition (Schmidt theorem), any entangled (unfactorable) bipartite wave function can be presented as a sum of factorized terms.
“A natural extension of this definition is given by the Schmidt decomposition, or Schmidt theorem [14,15], according to which any entangled (unfactorable) bipartite wave function can be presented as a sum of factorized terms.”
From Entanglement of biphoton states: qutrits and ququarts (2011) · cites this paper as [15]
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Entanglement of biphoton states: qutrits and ququarts
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- Authors
- Ekert, A., & Knight, P. L.
- Affiliations
- University of Oxford (GB)
- University of Konstanz (DE)
- Venue
- American Journal of Physics
- Published
- 1995-05-01
- Volume
- 63
- Issue
- 5
- Pages
- 415-423
- ISSN
- 0002-9505 (ISSN-L)
- 1943-2909
- OpenAlex
- W1970948880
- Cited by
- 453
- References
- 0
- Citations by year
- 2026: 17 · 2025: 23 · 2024: 28 · 2023: 21 · 2022: 37 · 2021: 21 · 2020: 17 · 2019: 14 · 2018: 13 · 2017: 12 · 2016: 21 · 2015: 8 · 2014: 16 · 2013: 16 · 2012: 19
- FWCI
- 6.17
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Journal of Physics (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- 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 optics and atomic interactions
- Keywords
- quantum entanglement, Schmidt decomposition, two-mode squeezed states, atom-field interaction, quantum optics, orthonormal bases
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