Bounds on the Information Rate of Quantum Secret Sharing Schemes

TL;DR

This paper establishes new upper bounds on the information rate of quantum secret sharing schemes, showing that some schemes cannot achieve high rates and extending classical bounds to the quantum domain.

Contribution

It derives the first non-trivial upper bounds on quantum secret sharing information rates, generalizing classical bounds to quantum access structures.

Findings

Existence of quantum access structures with information rate at most O((log n)/n)

Information rate cannot always be one in quantum secret sharing schemes

Provides bounds analogous to classical secret sharing bounds by Csirmaz

Abstract

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.