Entanglement of a pair of quantum bits
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The ``entanglement of formation'' of a mixed state \ensuremath{\rho} of a bipartite quantum system can be defined as the minimum number of singlets needed to create an ensemble of pure states that represents \ensuremath{\rho}. We find an exact formula for the entanglement of formation for all mixed states of two qubits having no more than two nonzero eigenvalues, and we report evidence suggesting that the formula is valid for all states of this system.
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The matrix τ defined here coincides with that introduced in Eq. (38) in the 2×2 case.
“The relation between the present and the original approach to concurrence [27,57] becomes apparent with the observation that the matrix τ defined here coincides with that introduced in Eq. (38)”
From Measures and dynamics of entangled states (2005) · cites this paper as [57]
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Entanglement of Formation of Bipartite Quantum States
Chen, K., Albeverio, S. A., & Fei, S.-M. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.210501 · Cited by 150 · see citing works
Quantum correlations and coherence in spin-1 Heisenberg chains
Malvezzi, A. L., Karpat, G., Çakmak, B., Fanchini, F. F., Debarba, T., & Vianna, R. O. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.184428 · Cited by 145 · see citing works
Measuring coherence with entanglement concurrence
Qi, X., Gao, T., & Yan, F. (2017) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aa7638 · Cited by 147 · see citing works
Volz, J., Scheucher, M., Junge, C., & Rauschenbeutel, A. (2014) · Nature Photonics · doi:10.1038/nphoton.2014.253 · Cited by 143 · see citing works
- Authors
- Hill, S., & Wootters, W. K.
- Affiliations
- Williams College (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1997-06-30
- Volume
- 78
- Issue
- 26
- Pages
- 5022-5025
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2073781628
- Cited by
- 2,823
- References
- 18
- Citations by year
- 2026: 102 · 2025: 141 · 2024: 127 · 2023: 165 · 2022: 126 · 2021: 132 · 2020: 92 · 2019: 108 · 2018: 92 · 2017: 117 · 2016: 134 · 2015: 110 · 2014: 116 · 2013: 93 · 2012: 103
- FWCI
- 17.04
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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 many-body systems
- Keywords
- entanglement of formation, two-qubit systems, mixed states, singlets, bipartite quantum systems, exact formulas, quantum entanglement
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