The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
Entanglement of a Pair of Quantum Bits
Open accessAbstract
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Quantum cryptography based on Bell’s theorem
Ekert, A. K. (1991) · Physical Review Letters · doi:10.1103/physrevlett.67.661 · Cited by 10,777
Mixed-state entanglement and quantum error correction
Bennett, C. H., DiVincenzo, D. P., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review A · doi:10.1103/physreva.54.3824 · Cited by 5,272
Self-citationSeparability Criterion for Density Matrices
Peres, A. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.1413 · Cited by 5,191
Separability of mixed states: necessary and sufficient conditions
Horodecki, M., Horodecki, P., & Horodecki, R. (1996) · Physics Letters A · doi:10.1016/s0375-9601(96)00706-2 · Cited by 3,649
Concentrating partial entanglement by local operations
Bennett, C. H., Bernstein, H. J., Popescu, S., & Schumacher, B. W. (1996) · Physical Review A · doi:10.1103/physreva.53.2046 · Cited by 3,151
Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
Bennett, C. H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.722 · Cited by 2,961
Self-citationQuantum cryptography without Bell’s theorem
Bennett, C. H., Brassard, G., & Mermin, N. D. (1992) · Physical Review Letters · doi:10.1103/physrevlett.68.557 · Cited by 2,536
Vedral, V., Plenio, M. B., Rippin, M. A., & Knight, P. L. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.2275 · Cited by 1,967
Fidelity for Mixed Quantum States
Jozsa, R. (1994) · Journal of Modern Optics · doi:10.1080/09500349414552171 · Cited by 1,911
Varberg, D. E. (1973) · Cited by 1,700
DiVincenzo, D. P. (1995) · Science · doi:10.1126/science.270.5234.255 · Cited by 1,651
The ‘transition probability’ in the state space of a—algebra
Uhlmann, A. (1976) · Reports on Mathematical Physics · doi:10.1016/0034-4877(76)90060-4 · Cited by 1,649
Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels
Deutsch, D., Ekert, A., Jozsa, R., Macchiavello, C., Popescu, S., & Sanpera, A. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.2818 · Cited by 1,268
Information-theoretic aspects of inseparability of mixed states
Horodecki, R., & Horodecki, M. (1996) · Physical Review A · doi:10.1103/physreva.54.1838 · Cited by 576
Inseparable Two Spin-12Density Matrices Can Be Distilled to a Singlet Form
Horodecki, M., Horodecki, P., & Horodecki, R. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.574 · Cited by 402
Teleportation, Bell's inequalities and inseparability
Horodecki, R., Horodecki, M., & Horodecki, P. (1996) · Physics Letters A · doi:10.1016/0375-9601(96)00639-1 · Cited by 279
Collective tests for quantum nonlocality
Peres, A. (1996) · Physical Review A · doi:10.1103/physreva.54.2685 · Cited by 179
Resource letter IQM-2: Foundations of quantum mechanics since the Bell inequalities
Ballentine, L. E. (1987) · American Journal of Physics · doi:10.1119/1.14988 · Cited by 66
Flagged first, then by citations
Research works printed but not linked: 1
- D. Bures, 1969, Trans. Am. Math. Soc., 135, 199
Cited by
Sorted by citations
Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.865 · Cited by 10,118
Entanglement of Formation of an Arbitrary State of Two Qubits
Wootters, W. K. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.2245 · Cited by 8,290
Self-citationEntanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745
Coffman, V., Kundu, J., & Wootters, W. K. (2000) · Physical Review A · doi:10.1103/physreva.61.052306 · Cited by 2,619
Self-citationGühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401
Metadata
- 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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
