Influence Of The Channel State On Cloning And UNOT Gate

Quantum information science is a comprehensive subject, that is a synthesis of many natural sciences including information science, mathematics and other subjects. In a society of information, quantum communication has also been received extensive attention. Quantum information comprises information theory, quantum teleportation, quantum entanglement, quantum cloning, and key distribution etc. Quantum cloning has been studied from different angles, and universal quantum cloning, probabilistic cloning, symmetric discrete quantum cloning, cloning of continuous quantum variables have been proposed. No-cloning theorem forbids the perfect cloning of unknown quantum state, and is a foundation of quantum communication. Although quantum no-cloning theorem prohibits exact cloning for the unknown quantum states, yet the quantum no-cloning theorem does not ban no-perfect cloning. In this thesis we focus our attention on quantum cloning. Based on a protocol of quantum cloning via teleportation with a maximally entangled quantum channel, we study the fidelity of quantum cloning and the fidelity of flipping state in the situation of a general no-maximally entangled quantum channel.The first chapter introduces the basic of quantum information, including C-NOT gate, the density operator, the protocol of quantum teleportation and its implementation, and the generation of Bell states.The second chapter describes quantum no-cloning theorem, the meaning of no-cloning theorem, the universal quantum copying machine. We also provide a protocol to realize quantum cloning and flipping the remote quantum state by using quantum teleportation with a maximally entangled quantum channel.The third and fourth chapters we discuss the situation where the quantum channel is not in a maximally entangled state. The influence of the quantum channel on cloning and UNOT gate is analyzed. The fidelity of quantum cloning and fidelity of flipping quantum state are expressed as a function of the coefficients of the quantum channel state. In the fifth chapter, we give varieties of fidelity of the quantum cloning and fidelity of flipping quantum state for different projective subspaces and quantum channels.