Entanglement Sharing Scheme via quantum error correcting code

Quantum secret sharing concerns secure and reliable distribution of classical or quantum information by a dealer to a set of ¡°players¡± such that authorized subsets can access full information and unauthorized subsets are denied any information whatsoever. Ramp secret sharing reduces bandwidth requirements by reducing the size of shares to individual players but at a cost of leaking some information to unauthorized subsets of players. Although quantum ramp secret sharing has been studied, to date there has not been a systematic way to classify information leakage. We introduce a security condition based on our new protocol of ¡°entanglement sharing¡± wherein half of maximally entangled bipartite shares are encrypted into multipartite states in such a way that unauthorized players can only establish shared separable (not entangled) states with the dealer. Only authorized subsets of players obtain entangled states, which enable quantum information tasks such as teleportation. Our scheme can reduce share sizes by half to improve efficiency as we show with the [[4,2,2]] stabilizer encoding to establish a threshold entanglement sharing scheme. Finally we establish that any quantum error-correcting code can be used for entanglement sharing with the support of perfect classical secret sharing.