Details
| Original language | English |
|---|---|
| Article number | 052333 |
| Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
| Volume | 81 |
| Issue number | 5 |
| Publication status | Published - 24 May 2010 |
| Externally published | Yes |
Abstract
A secret-sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret-sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret-sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum-secret-sharing schemes. In addition to providing a new perspective on quantum-secret-sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum-secret-sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum-secret-sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure-state quantum-secret-sharing scheme with information rate 1.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
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In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 81, No. 5, 052333, 24.05.2010.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Matroids and quantum-secret-sharing schemes
AU - Sarvepalli, Pradeep
AU - Raussendorf, Robert
PY - 2010/5/24
Y1 - 2010/5/24
N2 - A secret-sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret-sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret-sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum-secret-sharing schemes. In addition to providing a new perspective on quantum-secret-sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum-secret-sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum-secret-sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure-state quantum-secret-sharing scheme with information rate 1.
AB - A secret-sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret-sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret-sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum-secret-sharing schemes. In addition to providing a new perspective on quantum-secret-sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum-secret-sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum-secret-sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure-state quantum-secret-sharing scheme with information rate 1.
UR - http://www.scopus.com/inward/record.url?scp=77953142850&partnerID=8YFLogxK
U2 - 10.48550/arXiv.0909.0549
DO - 10.48550/arXiv.0909.0549
M3 - Article
AN - SCOPUS:77953142850
VL - 81
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1094-1622
IS - 5
M1 - 052333
ER -