An important metric of the performance of a quantum-secret-sharing scheme is its information rate. Beyond the fact that the information rate is upper-bounded by one, very little is known in terms of bounds on the information rate of quantum-secret-sharing schemes. Furthermore, not every scheme can be realized with rate one. In this paper we derive upper bounds for the information rates of quantum-secret-sharing schemes. We show that there exist quantum access structures on $n$ players for which the information rate cannot be better than $O((\log {}_{2}n)/n)$. These results are the quantum analogues of the bounds for classical-secret-sharing schemes proved by Csirmaz.

• Received 13 December 2010

DOI:https://doi.org/10.1103/PhysRevA.83.042324