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Matroids and quantum-secret-sharing schemes

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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  • University of British Columbia

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OriginalspracheEnglisch
Aufsatznummer052333
FachzeitschriftPhysical Review A - Atomic, Molecular, and Optical Physics
Jahrgang81
Ausgabenummer5
PublikationsstatusVeröffentlicht - 24 Mai 2010
Extern publiziertJa

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.

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Matroids and quantum-secret-sharing schemes. / Sarvepalli, Pradeep; Raussendorf, Robert.
in: Physical Review A - Atomic, Molecular, and Optical Physics, Jahrgang 81, Nr. 5, 052333, 24.05.2010.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Sarvepalli P, Raussendorf R. Matroids and quantum-secret-sharing schemes. Physical Review A - Atomic, Molecular, and Optical Physics. 2010 Mai 24;81(5):052333. doi: 10.48550/arXiv.0909.0549, 10.1103/PhysRevA.81.052333
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