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Graphical description of the action of local Clifford transformations on graph states
Open accessAbstract
We translate the action of local Clifford operations on graph states into transformations on their associated graphs, i.e., we provide transformation rules, stated in purely graph theoretical terms, which completely characterize the evolution of graph states under local Clifford operations. As we will show, there is essentially one basic rule, successive application of which generates the orbit of any graph state under local unitary operations within the Clifford group.
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“The state | Φ ˆ θ 〉 △ is obtained via local complementation [44] on qubit 2 of | Φ ˆ θ 〉 ⊂ .”
From Demonstration of Blind Quantum Computing (2012) · cites this paper as [44]
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Metadata
- Authors
- Van den Nest, M., Dehaene, J., & De Moor, B.
- Affiliations
- KU Leuven (BE)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2004-02-24
- Volume
- 69
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2165148883
- Cited by
- 335
- References
- 8
- Citations by year
- 2026: 14 · 2025: 34 · 2024: 25 · 2023: 21 · 2022: 19 · 2021: 22 · 2020: 16 · 2019: 15 · 2018: 11 · 2017: 8 · 2016: 13 · 2015: 6 · 2014: 8 · 2013: 9 · 2012: 12
- FWCI
- 14.54
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- graph states, Clifford group, local unitary operations, graph transformation, quantum error correction, graph theory
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