The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
How to Share a Quantum Secret
Open accessAbstract
We investigate the concept of quantum secret sharing. In a $(k,n)$ threshold scheme, a secret quantum state is divided into $n$ shares such that any $k$ of those shares can be used to reconstruct the secret, but any set of $k\ensuremath{-}1$ or fewer shares contains absolutely no information about the secret. We show that the only constraint on the existence of threshold schemes comes from the quantum ``no-cloning theorem,'' which requires that $n<2k$, and we give efficient constructions of all threshold schemes. We also show that, for $k\ensuremath{\le}n<2k\ensuremath{-}1$, then any $(k,n)$ threshold scheme must distribute information that is globally in a mixed state.
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“The unique feature of this specific code is that there exist encoded operators (also referred to as logical operators in the literature) that have support only on two of the three qutrits that constitute the encoded space.Furthermore, it is then possible to identify sets of encoded operators that have the same action on the codespace, but have nontrivial support on different pairs of qutrits.”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [177]
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“The erasure-correcting property of this code ensures that any three-qutrit state within the codespace can be reconstructed even if one of the three qutrits is lost or erased.”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [177]
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“Secondly, from any two of the qutrits Bob can reconstruct the state.”
From Bulk locality and quantum error correction in AdS/CFT (2015) · cites this paper as [25]
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“First of all for any state | ˜ ψ 〉 , the reduced density matrix on any one of the qutrits is maximally mixed.”
From Bulk locality and quantum error correction in AdS/CFT (2015) · cites this paper as [25]
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“Thus 3 and 15 analyzer settings are respectively required to obtain the single- [28] and two-photon Stokes parameters.”
From Nonmaximally Entangled States: Production, Characterization, and Utilization (1999) · cites this paper as [28]
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Citations
Cites
Shamir, A. (1979) · Communications of the ACM · doi:10.1145/359168.359176 · Cited by 13,756
A single quantum cannot be cloned
Wootters, W. K., & Zurek, W. H. (1982) · Nature · doi:10.1038/299802a0 · Cited by 5,406 · cited 2×
“This contradicts the “no-cloning theorem” [11,12].”
BackgroundMixed-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
Scheme for reducing decoherence in quantum computer memory
Shor, P. W. (1995) · Physical Review A · doi:10.1103/physreva.52.r2493 · Cited by 4,479
Safeguarding cryptographic keys
BLAKLEY, G. R. (1979) · 1979 International Workshop on Managing Requirements Knowledge (MARK) · doi:10.1109/mark.1979.8817296 · Cited by 3,499
Hillery, M. S., Bužek, V., & Berthiaume, A. (1999) · Physical Review A · doi:10.1103/physreva.59.1829 · Cited by 3,391
Error Correcting Codes in Quantum Theory
Steane, A. M. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.793 · Cited by 2,677
Quantum 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 2,525
Good quantum error-correcting codes exist
Calderbank, A. R., & Shor, P. W. (1996) · Physical Review A · doi:10.1103/physreva.54.1098 · Cited by 2,516
Theory of quantum error-correcting codes
Knill, E., & Laflamme, R. (1997) · Physical Review A · doi:10.1103/physreva.55.900 · Cited by 1,593
Flagged first, then by citations
Research works printed but not linked: 2
- G. Blakely, 1979, Proceedings of the National Computer Conference, New York, 1979
- D. Aharonov, 1998, Proceedings of the 29th ACM Symposium on Theory of Computing
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The security of practical quantum key distribution
Scarani, V., Bechmann-Pasquinucci, H., Cerf, N. J., Dušek, M., Lütkenhaus, N., & Peev, M. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.1301 · Cited by 3,870
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
Advances in quantum cryptography
Pirandola, S., Andersen, U. L., Banchi, L., Berta, M., Bunandar, D., Colbeck, R., Englund, D., Gehring, T., Lupo, C., Ottaviani, C., et al. (2020) · Advances in Optics and Photonics · doi:10.1364/aop.361502 · Cited by 2,033
Secure quantum key distribution with realistic devices
Xu, F., Ma, X., Zhang, Q., Lo, H., & Pan, J.-W. (2020) · Reviews of Modern Physics · doi:10.1103/revmodphys.92.025002 · Cited by 1,649
Self-citationHolographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
Pastawski, F., Yoshida, B., Harlow, D., & Preskill, J. (2015) · Journal of High Energy Physics · doi:10.1007/jhep06(2015)149 · Cited by 958
Metadata
- Authors
- Cleve, R., Gottesman, D., & Lo, H.-K.
- Affiliations
- University of Calgary (CA)
- Los Alamos National Laboratory (US)
- Hewlett-Packard (United Kingdom) (GB)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1999-07-19
- Volume
- 83
- Issue
- 3
- Pages
- 648-651
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2083019346
- Cited by
- 1,373
- References
- 25
- Citations by year
- 2026: 43 · 2025: 87 · 2024: 63 · 2023: 56 · 2022: 38 · 2021: 66 · 2020: 65 · 2019: 64 · 2018: 72 · 2017: 56 · 2016: 51 · 2015: 64 · 2014: 60 · 2013: 69 · 2012: 65
- FWCI
- 14.90
- 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 › Computer Science › Computer Networks and Communications › Cryptography and Data Security
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- quantum secret sharing, threshold schemes, no-cloning theorem, quantum information, secret reconstruction, mixed states, quantum cryptography, information distribution
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