Going beyond the share size bound in quantum secret sharing

Quantum secret sharing (QSS) is an important cryptographic protocol which allows a quantum secret to be split between multiple "players", such that only certain authorised player subsets may recover the secret. It is, however, costly in terms of quantum communication and storage; perfect QSS using quantum states requires every player's share to be at least as large as the original secret. I will discuss some of our recent results in which we improve upon this bound through the use of imperfect "ramp" secret sharing, which allows for smaller shares at the cost of weaker security. We find a specific class of "entanglement sharing" ramp protocols, which allow for smaller shares while still broadly restricting the protocols' information leakage. Finally I will demonstrate how, by incorporating classical encryption into "hybrid" QSS protocols, quantum share size can be reduced (sometimes drastically) without requiring any reduction in security.