Study Of Quantum Operation Sharing With Bell States And W States

Quantum information science is an inter-discipline of quantum mechanics and information science. Quantum operation sharing (QOS) is one of the important research fields in the discipline. In this paper we will show nine tripartite QOS schemes we proposed by using W states and Bell states as quantum channels. The main research content includes:(1) Two tripartite QOS schemes for sharing an initial performer’s single-qubit operation on a target qubit in remote agents’site, are put forward with local operation and classical communication as well as shared entanglements. The first scheme uses a Bell state and a symmetric W state as quantum channels, while the second one utilizes a Bell state and an asymmetric W state instead. Both schemes are applicable for achieving the initial performer’s operation on a target qubit in remote sharers’qubit. The first scheme is probabilistic while the second one in deterministic. Both schemes are treated and compared from the five aspects of quantum resource consumption, operation complexity, classical resource consumption, success probability and efficiency. It is found that, except that they consume same quantum resources, the latter scheme is more superior than the former one concerning last four aspects.(2) Two tripartite schemes for sharing a single-qubit operation on a remote qubit are proposed with symmetric and asymmetric W states, respectively. They are treated and compared from the aspects of quantum resource consumption, operation complexity, classical resource consumption, success probability and efficiency. It is found that, except for same quantum resource consumptions, the first scheme is overall better than the second one.(3) Tripartite remote sharing of any single-qubit operation with two asymmetric threequbit W states is amply treated. Five schemes are put forward with the W states in five different entanglement structures corresponding to five different distributions of two identical qubit trios in three locations. For all schemes, two features about the security and the agent symmetry are analyzed and confirmed. Moreover, resource consumption, necessary-operation complexity, success probability and efficiency are also worked out and compared mutually. Quantum resource consumption and necessary-operation complexity are same for all schemes. Nonetheless, four schemes each consume less classical resources, while they are probabilistic and own lower efficiencies. One schemes needs to cost two additional classical bits, however, it is deterministic and has higher efficiencies. It is found that, both the success probability and the intrinsic efficiency of each scheme are completely determined by the corresponding entanglement structure of the two W states. The underlying physics of this feature is revealed. In addition, the implementation feasibility of all the schemes is also confirmed according to the current experimental techniques.