Study Of Single-qubit Operation Sharing With Some Quantum Entangled States

Quantum information science is a new cross subject, which is based on quantum states of microscopic system as an information carrier, and uses the basic principles of quantum mechanics for encoding information, communication and computation processing. The subject in both theory and experiment has achieved a major breakthrough in recent years. Quantum operation sharing (QOS) is a new branch of the research in the field. According to the branch, we will focus on studying single-qubit quantum operation sharing using some entangled states as quantum channels. The main contents are as follows:(1) We generalize the last two schemes in [J.Phys.B 44 (2011) 165508]. Specifically, we use a pair of Bell state and a GHZ state to respectively present corresponding generalized schemes. Compared to the previous schemes, we add another six restricted sets of single-qubit quantum operations in the generalized schemes. That is, we accomplish eight restricted sets of operations sharing in total in the two schemes. We make comparisons of the two schemes from the following four aspects:the cost of quantum and classical resources, the difficulty or intensity of necessary operations, and the intrinsic efficiency. It is found that the scheme which uses a GHZ state as a quantum channel is more superior and economic than the scheme which utilizes a pair of Bell state as quantum channels.(2) Using five-qubit cluster state as a quantum channel, we study the capacity of the state in different entanglement structures for sharing single-qubit operation among tripartite. Through investigation, we find that there exist two kinds of entanglement structures of the state can be suitable for sharing quantum operation. The intrinsic reason is that cluster state in these two entanglement structures can be transformed to a Bell state and a GHZ state (or a controlled Bell state) by performing some local unitary operations. The former can be used as quantum channel to achieve the quantum state teleportation, the latter can be used to fulfill the quantum state sharing.(3) Using a six-qubit cluster state as a quantum channel, we firstly present a four-party quantum operation sharing scheme. We further explore the underlying physics why six-qubit cluster state can be applicable for deterministically fulfilling four-party single-qubit operation sharing. We find that six-qubit cluster state in a peculiar entanglement structure can be transformed a product state of a Bell state and a controlled GHZ state by performing some local unitary operations. The product state can be suitable for fulfilling the quantum task. In addition, we discuss the scheme and assure that the scheme is secure and feasible according to the present experimental technologies.