Controllability Aspects of The Lindblad-Kossakowski Master Equation

[1]  Uwe Helmke,et al.  The dynamics of open quantum systems: accessibility results , 2007 .

[2]  A. Holevo Statistical structure of quantum theory , 2001 .

[3]  Bernard Bonnard,et al.  Transitivity of families of invariant vector fields on the semidirect products of Lie groups , 1982 .

[4]  Timo O. Reiss,et al.  Optimal control of spin dynamics in the presence of relaxation. , 2002, Journal of magnetic resonance.

[5]  University of Toronto,et al.  Conditions for strictly purity-decreasing quantum Markovian dynamics , 2006 .

[6]  Velimir Jurdjevic,et al.  Control systems on semi-simple Lie groups and their homogeneous spaces , 1981 .

[7]  K. Dekimpe,et al.  TRANSLATIONS IN SIMPLY TRANSITIVE AFFINE ACTIONS OF FREE 2-STEP NILPOTENT LIE GROUPS , 2006 .

[8]  C. Altafini,et al.  Quantum Markovian master equation driven by coherent controls: a controllability analysis , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[9]  Jonathan P Dowling,et al.  Quantum technology: the second quantum revolution , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[10]  D. Montgomery,et al.  Transformation Groups of Spheres , 1943 .

[11]  Li-Chen Fu,et al.  Controllability of spacecraft systems in a central gravitational field , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[12]  Burkhard Luy,et al.  Boundary of quantum evolution under decoherence , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Velimir Jurdjevic,et al.  Controllability properties of affine systems , 1984, The 23rd IEEE Conference on Decision and Control.

[14]  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.

[15]  S. Helgason Differential Geometry, Lie Groups, and Symmetric Spaces , 1978 .

[16]  D. D’Alessandro,et al.  Small time controllability of systems on compact Lie groups and spin angular momentum , 2001 .

[17]  V. Jurdjevic Geometric control theory , 1996 .

[18]  Uwe Helmke,et al.  Lie Theory for Quantum Control , 2008 .

[19]  S. Schirmer,et al.  Orbits of quantum states and geometry of Bloch vectors for N-level systems , 2003, quant-ph/0308004.

[20]  J. Hilgert,et al.  Lie groups, convex cones, and semigroups , 1989 .

[21]  E. Sudarshan,et al.  Completely Positive Dynamical Semigroups of N Level Systems , 1976 .

[22]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[23]  Jacques Tits Tabellen zu den einfachen Lie Gruppen und ihren Darstellungen , 1967 .

[24]  D. Tannor,et al.  Phase space approach to theories of quantum dissipation , 1997 .

[25]  A. Baker Matrix Groups: An Introduction to Lie Group Theory , 2003 .

[26]  R. Brockett Lie Theory and Control Systems Defined on Spheres , 1973 .

[27]  L. Grüne Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization , 2002 .

[28]  Domenico D'Alessandro,et al.  Notions of controllability for bilinear multilevel quantum systems , 2003, IEEE Trans. Autom. Control..

[29]  William M. Boothby,et al.  A transitivity problem from control theory , 1975 .

[30]  E. B. Davies Quantum theory of open systems , 1976 .

[31]  Dionisis Stefanatos,et al.  Relaxation-optimized transfer of spin order in Ising spin chains (6 pages) , 2005 .

[32]  P. Krishnaprasad,et al.  Control Systems on Lie Groups , 2005 .

[33]  Uwe Helmke,et al.  Spin Dynamics: A Paradigm for Time Optimal Control on Compact Lie Groups , 2006, J. Glob. Optim..

[34]  A. W. Knapp Lie groups beyond an introduction , 1988 .

[35]  A. I. Solomon,et al.  Controllability of Quantum Systems , 2003 .

[36]  Domenico D'Alessandro,et al.  Topological properties of reachable sets and the control of quantum bits , 2000 .

[37]  Man-Duen Choi Completely positive linear maps on complex matrices , 1975 .

[38]  G. Bodenhausen,et al.  Principles of nuclear magnetic resonance in one and two dimensions , 1987 .

[39]  Uwe Helmke,et al.  Lie-semigroup structures for reachability and control of open quantum systems: kossakowski-lindblad generators form lie wedge to markovian channels , 2009 .

[40]  C. Altafini,et al.  QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC) 2357 Controllability properties for finite dimensional quantum Markovian master equations , 2002, quant-ph/0211194.

[41]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[42]  Two-transitive Lie groups , 2001, math/0106108.

[43]  Optimal control of coupled spin dynamics under cross-correlated relaxation , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[44]  U. Helmke,et al.  Optimization and Dynamical Systems , 1994, Proceedings of the IEEE.

[45]  William M. Boothby,et al.  Determination of the Transitivity of Bilinear Systems , 1979 .

[46]  Helmut Völklein,et al.  Transitivitätsfragen bei linearen Liegruppen , 1981 .

[47]  G. Lindblad On the generators of quantum dynamical semigroups , 1976 .

[48]  J. Swoboda Time-optimal Control of Spin Systems , 2006, quant-ph/0601131.

[49]  L. Fu,et al.  Controllability of spacecraft systems in a central gravitational field , 1994, IEEE Trans. Autom. Control..

[50]  Dionisis Stefanatos,et al.  Optimal control of coupled spins in presence of longitudinal and transverse relaxation , 2003, 2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775).

[51]  K. Kraus General state changes in quantum theory , 1971 .

[52]  K. Lendi,et al.  Quantum Dynamical Semigroups and Applications , 1987 .

[53]  Claudio Altafini,et al.  Coherent control of open quantum dynamical systems , 2004 .