Six-party (3, 5)-threshold quantum operation sharing with 8-qubit graph state

Quantum operation sharing (QOS) is an important quantum remote control technique, which can be used for remotely encrypting or decrypting quantum information. To date, all the sharers should collaborate to conclusively share the remote quantum operation in all the existing QOS schemes, which are the so-called (n, n)-threshold ones. In this paper, a six-party (3, 5)-threshold QOS scheme is put forward by utilizing an 8-qubit graph state, where 3 sharers among the 5 ones are able to achieve the sharing of the remote initial owner’s arbitrary operation. We investigated the symmetry and the limitation of the sharers who can reach the achievement, success probability, and its underlying physics, scheme security, and scheme feasibility. The scheme is observed to be secure, including that the quantum remote operation can be safely and successfully shared by any sharer with either two neighboring partners or two non-neighboring partners; moreover, the scheme is anticipated to be realized in the future according to the current technologies.