Quantum secret sharing with continuous variable graph state

In this paper, we study several physically feasible quantum secret sharing (QSS) schemes using continuous variable graph state (CVGS). Their implementation protocols are given, and the estimation error formulae are derived. Then, we present a variety of results on the theory of QSS with CVGS. Any $(k,n)$ threshold protocol of the three specific schemes satisfying $\frac{n}{2}<k\le n$ , where $n$ denotes the total number of players and $k$ denotes the minimum number of players who can collaboratively access the secret, can be implemented by certain weighted CVGS. The quantum secret is absolutely confidential to any player group with number less than threshold. Besides, the effect of finite squeezing to these results is properly considered. In the end, the duality between two specific schemes is investigated.