Quantum secret sharing and random hopping: Using single states instead of entanglement

Quantum secret sharing (QSS) protocols between N players, for sharing classical secrets, either use multipartite entangled states or use sequential manipulation of single d-level states only when d is prime (A. Tavakoli et al., arXiv: 1501.05582). We propose a sequential scheme which is valid for any value of d. In contrast to A. Tavakoli et al. whose efficiency (number of valid rounds) is 1/d, the efficiency of our scheme is 1/2 for any d. This, together with the fact that in the limit d -> infinity the scheme can be implemented by continuous variable optical states, brings the scheme into the domain of present day technology.