Effects of uncertainties and errors on Lyapunov control

Lyapunov control (open-loop) is often confronted with uncertainties and errors in practical applications. In this paper, we analyze the robustness of Lyapunov control against the uncertainties and errors in quantum control systems. The analysis is carried out through examinations of uncertainties and errors, calculations of the control fidelity under influences of the certainties and errors, as well as discussions on the caused effects. Two examples, a closed control system and an open control system, are presented to illustrate the general formulism.Comment: 4 pages, 5 figure

Nonmonotonic behavior of resistance in a superconductor-Luttinger liquid junction

Transport through a superconductor-Luttinger liquid junction is considered. When the interaction in the Luttinger liquid is repulsive, the resistance of the junction with a sufficiently clean interface shows nonmonotonic temperature- or voltage-dependence due to the competition between the superconductivity and the repulsive interaction. The result is discussed in connection with recent experiments on single-wall carbon nanotubes in contact with superconducting leads.Comment: Revtex4, 2 eps figure files, slightly revised from an earlier version submitted to PRL on 2001.12.

Mixed Qubit Cannot Be Universally Broadcast

We show that there does not exist any universal quantum cloning machine that can broadcast an arbitrary mixed qubit with a constant fidelity. Based on this result, we investigate the dependent quantum cloner in the sense that some parameter of the input qubit $\rho_s(\theta,\omega,\lambda)$ is regarded as constant in the fidelity. For the case of constant $\omega$, we establish the $1\to2$ optimal symmetric dependent cloner with a fidelity 1/2. It is also shown that the $1\to M$ optimal quantum cloning machine for pure qubits is also optimal for mixed qubits, when $\lambda$ is the unique parameter in the fidelity. For general $N\to M$ broadcasting of mixed qubits, the situation is very different.Comment: 5 pages, Revte