Equivalence between sharing quantum and classical secrets and error correction
Anne Marin, Damian Markham · Physical Review A · 2013
We present a general scheme for sharing quantum secrets, and an extension to sharing classical secrets, which contain all known quantum-secret-sharing schemes. In this framework, we show the equivalence of existence of both schemes, that is, the existence of a scheme sharing a quantum secret implies that the extended classical-secret-sharing scheme works, and vice versa. As a consequence of this, we find schemes sharing classical secrets for arbitrary access structures. We then clarify the relationship to quantum error correction and observe several restrictions thereby imposed, which for example indicates that for pure-state threshold schemes the share size $q$ must scale with the number of players $n$ as $q\ensuremath{\ge}\sqrt{n}$. These results also provide a way of searching for quantum-error-correcting codes.