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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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“This contradicts the “no-cloning theorem” [11,12].”
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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
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 ›
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