Sharing classical secrets with CSS codes

In this paper we investigate the use of quantum information to share classical secrets. While every quantum secret sharing scheme is a quantum error correcting code, the converse is not true. Motivated by this we sought to find quantum codes which can be converted to secret sharing schemes. If we are interested in sharing classical secrets using quantum information, then we show that a class of pure $[[n,1,d]]_q$ CSS codes can be converted to perfect secret sharing schemes. These secret sharing schemes are perfect in the sense the unauthorized parties do not learn anything about the secret. Gottesman had given conditions to test whether a given subset is an authorized or unauthorized set; they enable us to determine the access structure of quantum secret sharing schemes. For the secret sharing schemes proposed in this paper the access structure can be characterized in terms of minimal codewords of the classical code underlying the CSS code. This characterization of the access structure for quantum secret sharing schemes is thought to be new.