Approximate quantum state sharing via two private quantum channels

We investigate the approximate quantum state sharing protocol based on random unitary channels, which is secure against any exterior or interior attackers in principle. Although the protocol leaks small information for a security parameter $ϵ$, the scheme still preserves its information-theoretic secrecy, and reduces some pre-shared classical secret keys for a private quantum channel between a sender and two receivers. The approximate private quantum channels constructed via random unitary channels play a crucial role in the proposed quantum state sharing protocol.