Quantum secret sharing protocol using GHZ state: implementation on IBM qiskit

Quantum secret sharing is a way to share secret messages among several people using the quantum channel with unconditional security. Hillery et al. (Phys Rev A 59(3):1829, 1999) proposed the first quantum secret sharing protocol for three parties by using the 3-qubit GHZ states and a possible generalization of the protocol for four parties by using the 4-qubit GHZ states. Also in the same paper, they proposed a three-party secret-sharing scheme to share quantum states. Later Xiao et al. (Phys Rev A 69(5):052307, 2004) generalized the quantum secret sharing protocol for n parties to share a classical secret message. In this paper, we implement these protocols in IBM simulators as well as real backends and check security against some quantum attacks. Also, we create a noise model and simulate the protocols using the noise model. Finally, we use the zero noise extrapolation method to mitigate errors due to noise.