arXiv subjects

Jian-Wu Wu

Publications and source records attributed to Jian-Wu Wu.

4 recordsLinked to original sources

arXiv2007

Energy Optimal Control for Quantum System Evolving on SU(1,1)

This paper discusses the energy optimal control problem for the class of quantum systems that possess dynamical symmetry of SU(1,1), which are widely studied in various physical problems in the quantum theory. Based on the maximum principle on Lie group, the complete set of optimal controls are analytically obtained, including both normal and abnormal extremals. The results indicate that the normal extremal controls can be expressed by the Weierstrass elliptic function, while the abnormal extremal controls can only be constant functions of time t.

math.OC↗

arXiv2007

Controllability of Quantum Systems on the Lie Group SU(1,1)

This paper examines the controllability for quantum control systems with SU(1,1) dynamical symmetry, namely, the ability to use some electromagnetic field to redirect the quantum system toward a desired evolution. The problem is formalized as the control of a right invariant bilinear system evolving on the Lie group SU(1,1) of two dimensional special pseudo-unitary matrices. It is proved that the elliptic condition of the total Hamiltonian is both sufficient and necessary for the controllability. Conditions are also given for small time local controllability and strong controllability. The results obtained are also valid for the control systems on the Lie groups SO(2,1) and SL(2,R).

math.OC↗

arXiv2007

Asymptotically noise decoupling for Markovian open quantum systems

The noise decoupling problem is investigated for general N-level Markovian open quantum systems. Firstly, 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.

quant-ph↗

arXiv2005

Quasi multipartite entanglement measure based on quadratic functions

We develop a new entanglement measure by extending Jaeger's Minkowskian norm entanglement measure. This measure can be applied to a much wider class of multipartite mixed states, although still "quasi" in the sense that it is still incapable of dividing precisely the sets of all separable and entangled states. As a quadratic scalar function of the system density matrix, the quasi measure can be easily expressed in terms of the so-called coherence vector of the system density matrix, by which we show the basic properties of the quasi measure including (1) zero-entanglement for all separable states, (2) invariance under local unitary operations, and (3) non-increasing under local POVM (positive operator-valued measure) measurements. These results open up perspectives in further studies of dynamical problems in open systems, especially the dynamic evolution of entanglement, and the entanglement preservation against the environment-induced decoherence effects.

quant-ph↗