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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. 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 addition to providing a new perspective on quantum- secret-sharing schemes, this characterization has important benefits. In this paper we take the first steps toward a matroidal characterization of quantum- secret-sharing schemes. No such relations are known for quantum secret-sharing schemes. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. Classically, efficient secret-sharing schemes have been shown to be induced by matroids. International Nuclear Information System (INIS)Ī 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.

Matroids and quantum- secret-sharing schemes

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