Verifiable Quantum Secret Sharing Scheme Using d-dimensional GHZ State

In this paper we propose two verifiable threshold quantum secret sharing protocols with d-dimensional GHZ state. In the proposed protocol, the dealer Alice firstly divides all participants into two groups to achieve the two-line transmission. Then she randomly generates a three-qudit GHZ state, inserts the first two particles into two detecting photon sequences and sends them to participants in each group. In the distribution phase, each participant calculates and sends his commitment values to Alice by quantum secure direct communication. Furthermore, each participant performs a unitary operation on these received particles and sends them to the next participant using the decoy-photon technique. In the verification phase, Alice can perform two rounds of verification and test all participants’ honesty. In addition, we demonstrate our protocol to be secure against both eavesdropping and dishonest participants and compare our scheme with the existing schemes.