An information theoretical model for quantum secret sharing schemes

Similarly to earlier models for quantum error correcting codes, we introduce a quantum information theoretical model for quantum secret sharing schemes. This model provides new insights into the theory of quantum secret sharing. By using our model, among other results, we give a shorter proof of Gottesman's theorem that the size of the shares in a quantum secret sharing scheme must be as large as the secret itself. Also, we introduced approximate quantum secret sharing schemes and showed robustness of quantum secret sharing schemes by extending Gottesman's theorem to the approximate case.