The Theoretical Research On The Approximate Clone Of Entangled States

Quantum information theory is an interdiscipline subject of quantum mechanics and informatics, which has become one of the remarkable new science and developed very rapidly in recent years. Due to its unique properties in storage, transmission and operation that bring a qualitative leap to the storage capacity, communication security and computing power, quantum information will bring a great reformation for the information industry and become a new research hotspot. In 1982, the quantum no-cloning theorem was proved by Wootters and Zurek in a letter published in Nature.This theorem is a milestone in the development of quantum theory and ensured the safety of the quantum key distribution program.The quantum clone caught more and more interests until Buzek and Hillery proved the general quantum cloning program in1996 which greatly stimulated the scientific study of quantum cloning.Quantum entanglement as a important information resource of quantum information, Therefore study on quantum entanglement cloning becomes one of main direction quantum cloning research in recent years.This thesis firstly introduces the major categories of the quantum cloning and the national and foreign research progress in the quantum cloning field. Then the scheme of quantum remote cloning is employed to carry out a theoretical research of21? approximate cloning for the two-qubit entangled states and the three-qubit entangled states respectively, and obtained the following several aspects of the research results.Firstly, based on the quantum channel, the quantum cloning scheme of two-qubit Bell states and two-qubit unknown entangled states are researched. By taking advantage of the methods of the Bell basis unite measurement, Hadamard transformation and orthogonal measurement, the sender accomplished the quantum measurement for the particle, while the receiver restored the quantum state through unitary transformation and quantum logic gate. Then the fidelity of the cloning output was computed to be always five sixths.Secondly, based on the quantum channel, the unknown three-qubit GHZ states remote approximate 21? quantum cloning was researched. In the quantum measurement phase, there was twice Bell basis unite measurement. In the quantum restore phase, basing on different types of input, it introduce C-NOT gate and Toffoli gate successively, then designed two cloning schemes, accomplished the remote cloning for all types of unknown three-qubit GHZ states, computed the fidelity of output and confirmed the scheme mentioned to be the general cloning scheme.Thirdly, based on the two quantum channels, the scheme of quantum remote approximately cloning of the unknown three-qubit GHZ states was put forward. It was confirmed to be quantum cloning of constant phase by computing the fidelity of output.The calculated fidelity ranges from 21/36 to 25/36. This thesis also further researches the fidelity-input curve, discusses the advantages and disadvantages of the scheme of the one information channel and the two information channels, and makes theoretical basis for further research of the number choice on the entanglement remote cloning quantum channels.