Jian-Wu Wu

Publications (8)0 Total impact

• Article: Optimal bang-bang control for SU(1,1) coherent states

  Jian-Wu Wu, Chun-Wen Li, Tzyh-Jong Tarn, Jing Zhang
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  ABSTRACT: In this paper, the problem of achieving an arbitrary SU(1,1) coherent state is considered via switching the control field back and forth between admissible values with minimal number of switching times. When the controlled system Hamiltonian is hyperbolical or parabolical, the results show that the minimal switching number is one or two, which lies on whether the argument of the involved control is adjustable or not, and is independent of the target SU(1,1) coherent state. While for the elliptical case, the results indicate that the minimal number of switches needed depends on the target SU(1,1) coherent state and is provided as a function of it. In this case, one switch can also be saved if the argument of the involved control is adjustable. The theory developed here can also be extended to solve the optimal bang-bang control problem for a general SU(1,1) time evolution.
  Phys. Rev. A. 11/2007; 76(5).
• Source

  Available from: ArXiv

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

  Jian-Wu Wu, Chun-Wen Li, Jing Zhang, Tzyh-Jong Tarn
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  ABSTRACT: 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.
  10/2007;
• Source

  Available from: ArXiv

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

  Jian-Wu Wu, Chun-Wen Li, Jing Zhang, Tzyh-Jong Tarn
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  ABSTRACT: 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).
  09/2007;
• Article: Analytically solvable two-qubit entanglement monotone

  Jing Zhang, Chun-Wen Li, Tzyh-Jong Tarn, Jian-Wu Wu
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  ABSTRACT: A so-called quasientanglement measure was obtained [ J. Zhang et al. Phys. Rev. A 73 022319 (2006)] by extending Jaeger’s Minkowskian norm entanglement measure to general multipartite mixed states. The obtained quasientanglement measure has good properties, but it is still left open whether it is nonincreasing under general local operations and classical communications (LOCC). We show that the obtained quasientanglement measure is indeed nonincreasing on average under LOCC at least for two-qubit states. Thus, it is a good candidate for the two-qubit entanglement monotone. Further, it is shown that this entanglement measure is less than the concurrence for a large class of mixed entangled states.
  Phys. Rev. A. 09/2007; 76(3).
• Source

  Available from: arxiv.org

  Article: Asymptotically noise decoupling for Markovian open quantum systems

  Jing Zhang, Re-Bing Wu, Chun-Wen Li, Tzyh-Jong Tarn, Jian-Wu Wu
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  ABSTRACT: 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. Comment: 11 pages, 10 figures
  01/2007;
• Article: Quantum control by decomposition of SU(1, 1)

  Jian-Wu Wu, Chun-Wen Li, Re-Bing Wu, Tzyh-Jong Tarn, Jing Zhang
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  ABSTRACT: 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.
  Journal of Physics A General Physics 10/2006; 39(43):13531.
• Source

  Available from: arxiv.org

  Article: Quasi multipartite entanglement measure based on quadratic functions

  Jing Zhang, Chun-Wen Li, Re-Bing Wu, Tzyh-Jong Tarn, Jian-Wu Wu
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  ABSTRACT: 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. Comment: 10pages,1 figure
  12/2005;
• Source

  Available from: ArXiv

  Article: Quantum Fourier Transform in a Decoherence-Free Subspace

  Jian-Wu Wu, Chun-Wen Li, Re-Bing Wu
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  ABSTRACT: Quantum Fourier transform is of primary importance in many quantum algorithms. In order to eliminate the destructive effects of decoherence induced by couplings between the quantum system and its environment, we propose a robust scheme for quantum Fourier transform over the intrinsic decoherence-free subspaces. The scheme is then applied to the circuit design of quantum Fourier transform over quantum networks under collective decoherence. The encoding efficiency and possible improvements are also discussed.
  10/2004;