Lie Theory for Quantum Control
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Uwe Helmke | G. Dirr | U. Helmke | G. Dirr
[1] Navin Khaneja,et al. Optimal experiments for maximizing coherence transfer between coupled spins. , 2005, Journal of magnetic resonance.
[2] R. Westwick,et al. A theorem on numerical range , 1975 .
[3] G. Bodenhausen,et al. Principles of nuclear magnetic resonance in one and two dimensions , 1987 .
[4] Lawrence Markus. Control dynamical systems , 2005, Mathematical systems theory.
[5] John B. Moore,et al. Gradient Flows Computing the C-numerical Range with Applications in NMR Spectroscopy , 2002, J. Glob. Optim..
[6] I. Chuang,et al. Quantum Computation and Quantum Information: Bibliography , 2010 .
[7] K. Gustafson,et al. Numerical Range: The Field Of Values Of Linear Operators And Matrices , 1996 .
[8] C. Altafini,et al. QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC) 2357 Controllability properties for finite dimensional quantum Markovian master equations , 2002, quant-ph/0211194.
[9] J. Hilgert,et al. Lie groups, convex cones, and semigroups , 1989 .
[10] Domenico D'Alessandro,et al. Notions of controllability for bilinear multilevel quantum systems , 2003, IEEE Trans. Autom. Control..
[11] Navin Khaneja,et al. Cartan decomposition of SU(2n) and control of spin systems , 2001 .
[12] Timo O. Reiss,et al. Optimal control of spin dynamics in the presence of relaxation. , 2002, Journal of magnetic resonance.
[13] University of Toronto,et al. Conditions for strictly purity-decreasing quantum Markovian dynamics , 2006 .
[14] Velimir Jurdjevic,et al. Control systems on semi-simple Lie groups and their homogeneous spaces , 1981 .
[15] U. Helmke,et al. Lie algebra representations, nilpotent matrices, and the C–numerical range , 2006 .
[16] William M. Boothby,et al. A transitivity problem from control theory , 1975 .
[17] H. Sussmann,et al. Control systems on Lie groups , 1972 .
[18] Jerzy Zabczyk,et al. Mathematical control theory - an introduction , 1992, Systems & Control: Foundations & Applications.
[19] J. Swoboda. Time-optimal Control of Spin Systems , 2006, quant-ph/0601131.
[20] Navin Khaneja,et al. Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer , 2002 .
[21] R. Brockett,et al. Time optimal control in spin systems , 2000, quant-ph/0006114.
[22] Dionisis Stefanatos,et al. Relaxation-optimized transfer of spin order in Ising spin chains (6 pages) , 2005 .
[23] Relative C -numerical ranges for applications in quantum control and quantum information , 2007, math-ph/0702005.
[24] G. Drobny,et al. Quantum Description of High‐Resolution NMR in Liquids , 1990 .
[25] R. Löwen,et al. Chapter 4 Compact projective planes , 1995 .
[26] A. Agrachev,et al. Control Theory from the Geometric Viewpoint , 2004 .
[27] Domenico D'Alessandro,et al. Controllability of One Spin and Two Interacting Spins , 2003, Math. Control. Signals Syst..
[28] E. B. Davies. Quantum theory of open systems , 1976 .
[29] Chi-Kwong Li,et al. C-numerical ranges and C-numerical radii , 1994 .
[30] A. Holevo. Statistical structure of quantum theory , 2001 .
[31] H. Sussmann,et al. Controllability of nonlinear systems , 1972 .
[32] O. Toeplitz. Das algebraische Analogon zu einem Satze von Fejér , 1918 .
[33] Domenico D'Alessandro,et al. The Lie algebra structure and controllability of spin systems , 2002 .
[34] C. Lobry. Controllability of Nonlinear Systems on Compact Manifolds , 1974 .
[35] S. Helgason. LIE GROUPS AND SYMMETRIC SPACES. , 1968 .
[36] F. Silva,et al. Controllability on classical Lie groups , 1988, Math. Control. Signals Syst..
[37] L. Fu,et al. Controllability of spacecraft systems in a central gravitational field , 1994, IEEE Trans. Autom. Control..
[38] Martin Kleinsteuber,et al. The Local C-Numerical Range: Examples, Conjectures, and Numerical Algorithms , 2006 .
[39] D. Montgomery,et al. Transformation Groups of Spheres , 1943 .
[40] Nam-Kiu Tsing,et al. The C-numerical range of matrices is star-shaped , 1996 .
[41] V. Jurdjevic. Geometric control theory , 1996 .
[42] Uwe Helmke,et al. The significance of the C -numerical range and the local C -numerical range in quantum control and quantum information , 2007, math-ph/0701035.
[43] Irreducible connected Lie subgroups of Gln(R) are closed , 1977 .
[44] Y. Poon. Another proof of a result of Westwick , 1980 .
[45] Claudio Altafini,et al. Coherent control of open quantum dynamical systems , 2004 .
[46] R. Brockett,et al. Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.
[47] MATRICES WITH CIRCULAR SYMMETRY ON THEIR UNITARY ORBITS AND C-NUMERICAL RANGES , 1991 .
[48] K. Hammerer,et al. Characterization of nonlocal gates , 2002 .
[49] Claudio Altafini,et al. Controllability of quantum mechanical systems by root space decomposition of su(N) , 2002 .
[50] S. Glaser,et al. Unitary control in quantum ensembles: maximizing signal intensity in coherent spectroscopy , 1998, Science.
[51] F. Hausdorff. Der Wertvorrat einer Bilinearform , 1919 .
[52] J. Gauthier,et al. Contrôlabilité des Systèmes Bilinéaires , 1982 .
[53] A. I. Solomon,et al. Controllability of Quantum Systems , 2003 .
[54] Dionisis Stefanatos,et al. Optimal control of coupled spins in the presence of longitudinal and transverse relaxation , 2004 .
[55] T. Tarn,et al. On the controllability of quantum‐mechanical systems , 1983 .
[56] Moshe Goldberg,et al. Elementary inclusion relations for generalized numerical ranges , 1977 .
[57] G. Lindblad. On the generators of quantum dynamical semigroups , 1976 .
[58] W. Thirring,et al. A Geometric picture of entanglement and Bell inequalities , 2001, quant-ph/0111116.
[59] U. Helmke,et al. A new type of C ‐numerical range arising in quantum computing , 2006 .
[60] V. Jurdjevic,et al. Control systems subordinated to a group action: Accessibility , 1981 .
[61] Time optimal factorizations on compact Lie groups , 2004 .
[62] J. Neumann. Mathematical Foundations of Quantum Mechanics , 1955 .
[63] E. Sudarshan,et al. Completely Positive Dynamical Semigroups of N Level Systems , 1976 .
[64] R. Brockett. Lie Theory and Control Systems Defined on Spheres , 1973 .
[65] Timo O. Reiss,et al. Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. , 2005, Journal of magnetic resonance.
[66] Two-transitive Lie groups , 2001, math/0106108.
[67] U. Helmke,et al. Optimization and Dynamical Systems , 1994, Proceedings of the IEEE.
[68] Ramakrishna,et al. Controllability of molecular systems. , 1995, Physical review. A, Atomic, molecular, and optical physics.
[69] A. G. Butkovskii,et al. Control of Quantum-Mechanical Processes and Systems , 1990 .
[70] William M. Boothby,et al. Determination of the Transitivity of Bilinear Systems , 1979 .
[71] Helmut Völklein,et al. Transitivitätsfragen bei linearen Liegruppen , 1981 .
[72] J. J. Sakurai,et al. Modern Quantum Mechanics , 1986 .
[73] Navin Khaneja,et al. On the Stochastic Control of Quantum Ensembles , 2000 .
[74] S. Helgason. Differential Geometry, Lie Groups, and Symmetric Spaces , 1978 .
[75] Uwe Helmke,et al. Spin Dynamics: A Paradigm for Time Optimal Control on Compact Lie Groups , 2006, J. Glob. Optim..