Dual quantum information splitting with degenerate graph states

Abstract: We propose a protocol for secret sharing, called dual quantum information splitting (DQIS), that reverses the roles of state and channel in standard quantum information splitting. In this method, a secret is shared via teleportation of a fiducial input state over an entangled state that encodes the secret in a graph state basis. By performing a test of violation of a Bell inequality on the encoded state, the legitimate parties determine if the violation is sufficiently high to permit distilling secret bits. Thus, the code space must be maximally and exclusively nonlocal. To this end, we propose two ways to obtain code words that are degenerate with respect to a Bell operator. The security of DQIS comes from monogamy of nonlocal correlations, which we illustrate by means of a simple single-qubit attack model. The nonlocal basis of security of our protocol makes it suitable for security in general monogamous theories and in the more stringent, device-independent cryptographic scenario.