Bounds on the Information Rate of Quantum Secret Sharing Schemes

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. Further, not every scheme can be realized with rate one. In this paper we derive new 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.