Entanglement sharing protocol via quantum error-correcting codes

We introduce a multiparty cryptographic protocol, which we call entanglement sharing schemes, wherein a dealer retains half of a maximally entangled bipartite state and encodes the other half into a multipartite state that is distributed among multiple players. In a close analog to quantum secret sharing, some subsets of players can recover maximal entanglement with the dealer whereas other subsets can recover no entanglement (though they may retain classical correlations with the dealer). We find a lower bound on the share size for such schemes and construct two nontrivial examples based on Shor's [[9,1,3]] and the [[4,2,2]] stabilizer code; we further demonstrate how other examples may be obtained from quantum error correcting codes through classical encryption. Finally, we demonstrate that entanglement sharing schemes can be applied to characterize leaked information in quantum ramp secret sharing.