Quantum Cloning And Schemes For Implementation Of Quantum Cloning In Experiment

This dissertation is devoted to the no-cloning theorem in quantum information. The deviation of the theorem is based on the basic constraint in quantum mechanics-the linearity of the Hilbert space. It points out that it is impossible to exactly copy an arbitrary unknown quantum state. Especially in the dissertation, the investigations are to the optimal approximate quantum cloning (including the universal quantum cloning and the phase-covariant quantum cloning), and the symmetry and asymmetry of the unitary transformations. Some schemes are also presented for the implementation of cloning and telecloning. The dissertation includes the following results.1): Investigations of quantum cloning(1): A novel and more concise proof is presented to derive simultaneously the unitary transformations of the optimal 1 →2 universal and phase-covariant quantum cloning in d-dimension. The deviations of the two unitary transformations were obtained through a great deal of paper in Physics Review A and Physics Review Letters from 1998 to 2003, and many constraints imposed as deviation. While we obtained them by only one natural demand, that is, the two fidelities at the output are equal. Starting by a unitary transformation with uncertain coefficients, the unitary transformation of the optimal universal quantum cloning is obtained as the information of the input state is completely unknown, and while the unitary transformation of the optimal phase-covariant quantum cloning is obtained as the information of the input state is partially unknown. The proof can be considered as a simpler way to understand better the optimal approximate quantum cloning.(2): We present a method to derive the unitary transformations of the optimal asymmetric approximate quantum cloning (the universal and phase-covariant quantum cloning). The method is more concise in comparison with N.J. Cerf's formalism to project single particle on the double-Bell basis. And the results obtained agree with the previous contributions. Further, the method offers an evidence to derive the unitary transformations of the optimal asymmetric approximate N → M quantum cloning in d-dimension.2): Schemes to implement the cloning and telecloning based on cavity QED.(1): We propose a scheme to implement the optimal symmetric general 1→2 phase-covariant quantum cloning in 2-dimension. The cloner is to clone the input state on the Bloch sphere with the amplitudes known and the phase unknown. In the process of cloning, the ancilla is required so that the unitary transformation of the cloner is symmetric. For cloning of states on the equator, i.e., the optimal phase-covariant quantum cloning, is subcloning of the cloner, therefore the cloner is so-called general phase-covariant quantum cloning. Due to the amplitudes, supposed known before cloning, being considered as parameters, the generalization is somehow difficult in mathematics. At present, there only exists the unitary transformation of the 1→2 phase-covariant quantum cloning in 2-dimension. The scheme we propose to implement the cloner is based on cavity QED.