Quantum Secret Sharing Schemes
نویسندگان
چکیده
Nascimento et al. [19] introduced a quantum information theoretical model for Quantum Secret Sharing (QSS) schemes. In this thesis, we describe existing schemes, such as the construction using Monotone Span Programs (MSPs) [16], according to this model. Moreover, the correctness of these schemes is proved in an information theoretical way. In particular, we consider the so-called pure state QSS schemes. We show that for these schemes, the recoverability and secrecy requirement are equivalent, which expands the theorem in [19]. Finally, we investigate the relationship between QSS schemes and quantum error correcting codes (QECCs). In [15], it was previously shown that Quantum Threshold Schemes (QTSs) can be constructed from quantum MDS codes. Here, we extend this theorem by formally proving that pure state QSS schemes are equivalent to quantum MDS codes. In addition, CSS codes and binary stabilizer codes are considered as a special case.
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