Approximate quantum state sharing via two private quantum channels

Abstract: 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 $\epsilon$, 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.