  We introduce a new 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
analogue 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 non-trivial
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.
