Matroids and quantum-secret-sharing schemes

verfasst von: Pradeep Sarvepalli, Robert Raussendorf
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.
Externe Organisation(en): University of British Columbia
Typ: Artikel
Journal: Physical Review A - Atomic, Molecular, and Optical Physics
Band: 81
ISSN: 1094-1622
Publikationsdatum: 24.05.2010
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Atom- und Molekularphysik sowie Optik
Elektronische Version(en): https://doi.org/10.48550/arXiv.0909.0549 (Zugang: Offen)
https://doi.org/10.1103/PhysRevA.81.052333 (Zugang: Geschlossen)

BibTeX

@article{462b6c61555345d5b76d59806eade9c7,
title = "Matroids and quantum-secret-sharing schemes",
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.",
author = "Pradeep Sarvepalli and Robert Raussendorf",
year = "2010",
month = may,
day = "24",
doi = "10.48550/arXiv.0909.0549",
language = "English",
volume = "81",
journal = "Physical Review A - Atomic, Molecular, and Optical Physics",
issn = "1094-1622",
publisher = "American Physical Society",
number = "5",
}