Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels
Open accessAbstract
Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on the quantum communication channel. Although they become operable if they are supplemented by classical privacy-amplification techniques, the resulting schemes are difficult to analyze and have not been proved secure. We introduce the concept of quantum privacy amplification and a cryptographic scheme incorporating it which is provably secure over a noisy channel. The scheme uses an ``entanglement purification'' procedure which, because it requires only a few quantum controlled-not and single-qubit operations, could be implemented using technology that is currently being developed.
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
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?
Entanglement distillation, concentration and purification are important tools to overcome noise in the quantum communication channel.
“An important tool to overcome the noise in the quantum communication channel is entanglement distillation, concentration and purification, proposed by Bennett et al. (1996aBennett et al. ( , 1996bBennett et al. ( , 1996c) ) and Deutsch et al. (1996).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Deutsch et al. (1996)
The Abstract (p. 1) describes an entanglement-purification procedure in a cryptographic scheme secure over a noisy quantum channel; the discussion on p. 4 explains how it produces nearly pure, maximally entangled pairs from mixed pairs. This supports purification as a way to address channel noise, but our copy does not establish entanglement concentration as a separate tool proposed by Deutsch et al. (LLM, conf=0.84)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
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 · see citing works
Self-citationQuantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
Werner, R. F. (1989) · Physical Review A · doi:10.1103/physreva.40.4277 · Cited by 4,062 · see citing works
Violating Bell inequality by mixed states: necessary and sufficient condition
Horodecki, R., Horodecki, P., & Horodecki, M. (1995) · Physics Letters A · doi:10.1016/0375-9601(95)00214-n · Cited by 884 · see citing works
Hidden quantum nonlocality revealed by local filters
Gisin, N. (1996) · Physics Letters A · doi:10.1016/s0375-9601(96)80001-6 · Cited by 531 · see citing works
Flagged first, then by citations
Research works printed but not linked: 2
- [1][1] C.H. Bennett and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing , Bangalore, India (IEEE, 1984) p. 175. -
- [4][4] C.H. Bennett, G. Brassard, and J.-M. Robert, SIAM J. Comp. 17 , 210 (1988); C.H. Bennett, G. Brassard, C. Cr´ epeau, and U.M. Maurer, 'Generalized privacy amplification', IEEE Trans. on Information Theory, Vol. IT-41, no. 6, November 1995, in press. -
Cited by
Sorted by citations
Gisin, N., Ribordy, G., Tittel, W., & Zbinden, H. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.145 · Cited by 8,515 · see citing works
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 · see citing works
Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication
Briegel, H.-J., Dür, W., Cirac, J. I., & Zoller, P. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.5932 · Cited by 3,481 · see citing works
Quantum information and computation
Bennett, C. H., & DiVincenzo, D. P. (2000) · Nature · doi:10.1038/35005001 · Cited by 3,263 · see citing works
Entanglement of a pair of quantum bits
Hill, S., & Wootters, W. K. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.5022 · Cited by 2,823 · see citing works
Quantum internet: a vision for the road ahead
Wehner, S., Elkouss, D., & Hanson, R. (2018) · Science · doi:10.1126/science.aam9288 · Cited by 2,467 · see citing works
Gühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401 · see citing works
Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network
Cirac, J. I., Zoller, P., Kimble, H. J., & Mabuchi, H. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.3221 · Cited by 2,215 · see citing works
Entanglement measures and purification procedures
Vedral, V., & Plenio, M. B. (1998) · Physical Review A · doi:10.1103/physreva.57.1619 · Cited by 1,419 · see citing works
Multiphoton entanglement and interferometry
Pan, J.-W., Chen, Z.-B., Lu, C.-Y., Weinfurter, H., Zeilinger, A., & Żukowski, M. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.777 · Cited by 1,410 · see citing works
“The main tool to overcome the noise in the quantum communication channel is entanglement purification, proposed by Bennett et al. (1996a, 1996b, 1996c) and Deutsch et al. (1996).”
InfluentialMultiple-particle interference and quantum error correction
(1996) · Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.1996.0136 · Cited by 1,284 · see citing works
General teleportation channel, singlet fraction, and quasidistillation
Horodecki, M., Horodecki, P., & Horodecki, R. (1999) · Physical Review A · doi:10.1103/physreva.60.1888 · Cited by 965 · see citing works
Topological Quantum Distillation
Bombin, H., & Martin-Delgado, M. A. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.180501 · Cited by 700 · see citing works
Bound entanglement can be activated
Horodecki, P., Horodecki, M., & Horodecki, R. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.1056 · Cited by 399 · see citing works
Classification of multiqubit mixed states: Separability and distillability properties
Dür, W., & Cirac, J. I. (2000) · Physical Review A · doi:10.1103/physreva.61.042314 · Cited by 291 · see citing works
Separability and Distillability of Multiparticle Quantum Systems
Dür, W., Cirac, J. I., & Tarrach, R. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.3562 · Cited by 279 · see citing works
The Universal Composable Security of Quantum Key Distribution
Ben-Or, M., Horodecki, M., Leung, D. W., Mayers, D., & Oppenheim, J. (2005) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-30576-7_21 · Cited by 227 · see citing works
Exponential Error Suppression for Near-Term Quantum Devices
Koczor, B. (2021) · Physical Review X · doi:10.1103/physrevx.11.031057 · Cited by 147 · see citing works
- Authors
- Deutsch, D., Ekert, A., Jozsa, R., Macchiavello, C., Popescu, S., & Sanpera, A.
- Affiliations
- University of Oxford (GB)
- University of Plymouth (GB)
- Boston University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1996-09-23
- Volume
- 77
- Issue
- 13
- Pages
- 2818-2821
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2063635674
- Cited by
- 1,268
- References
- 4
- Citations by year
- 2026: 47 · 2025: 90 · 2024: 52 · 2023: 53 · 2022: 39 · 2021: 54 · 2020: 35 · 2019: 43 · 2018: 33 · 2017: 44 · 2016: 45 · 2015: 40 · 2014: 54 · 2013: 42 · 2012: 58
- FWCI
- 31.54
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Bristol Research (University of Bristol) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Cryptography and Data Security
- Keywords
- quantum cryptography, noisy quantum channels, entanglement distillation, provable security, CNOT gate, single-qubit operations, quantum key distribution
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
