Jian- Wu

Asymptotically noise decoupling for Markovian open quantum systems

The noise decoupling problem is investigated for general N-level Markovian open quantum systems. First, the concept of Cartan decomposition of the Lie algebra su(N) is introduced as a tool of designing control Hamiltonians. Next, under certain assumptions, it is shown that a part of variables of the coherence vector of the system density matrix can be asymptotically decoupled from the environmental noises. The resulting noise decoupling scheme is applied to one-qubit, qutrit, and two-qubit quantum systems, by which the coherence evolution of the one-qubit and qutrit systems can always be asymptotically preserved, while, for two-qubit systems, our findings indicate that evolution of some variables can be preserved only for some initial states.

Quantum control by decomposition of SU(1, 1)

Constructive algorithms are presented for controlling quantum systems evolving on the SU(1, 1) Lie group. These procedures are performed via structured decomposition of SU(1, 1), which achieve precise controls without any approximations or iterative computations, under the sufficient condition that examines the existence of such decomposition. The technique is applied to controlling transitions between SU(1, 1) coherent states. These results open up new perspectives on the control design of infinite-dimensional quantum systems involving discrete or continuous spectra.