Characterization of majorization monotone quantum dynamics

IEEE Transactions on Automatic Control

Volumn 55, Issue 4, 2010, Pages 955-959

  Yuan, Haidong ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

Majorization; Open quantum dynamics

Indexed keywords

MAJORIZATION; MARKOVIAN ENVIRONMENT; OPEN QUANTUM SYSTEMS; QUANTUM DYNAMICS; SUFFICIENT CONDITIONS; TECHNICAL NOTES;

OPTIMIZATION; QUANTUM ELECTRONICS; QUANTUM OPTICS;

DYNAMICS;

EID: 77950795089     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2041619     Document Type: Article

References (44)

1. D. J. Tannor and S. A. Rice, "Control of selectivity of chemical reaction via control of wave packet evolution," J. Chem. Phys., vol.83, p. 5013, 1985.
2. D. J. Tannor, R. Kosloff, and S. A. Rice, "Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations," J. Chem. Phys., vol.85, p. 5805, 1986.
3. D. J. Tannor and S. A. Rice, "Coherent pulse sequence control of product formation in chemical reactions," Adv. Chem. Phys., vol.70, p. 441, 1988.
4. R. Kosloff, S. A. Rice, P. Gaspard, S. Tersigni, and D. J. Tannor, "Wavepacket dancing: Achieving chemical selectivity by shaping light pulses," Chem. Phys., vol.139, p. 201, 1989.
5. S. A. Rice and M. Zhao, Optical Control of Molecular Dynamics. New York: Wiley, 2000.
6. M. Shapiro and P. Brumer, Principles of the Quantum Control of Molecular Processes. New York: Wiley, 2003.
7. T. Brixner and G. Gerber, "Quantum control of gas-phase and liquidphase femtochemistry," Chem. Phys. Chem., vol.4, p. 418, 2003.
8. R. Mitrić, M. Hartmann, J. Pittner, and V. Bonačić- Koutecký, "New strategy for optimal control of femtosecond pump-dump processes," J. Phys. Chem. A, vol.106, p. 10477, 2002.
9. A. P. Peirce, M. A. Dahleh, and H. Rabitz, "Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications," Phys. Rev. A, vol.37, p. 4950, 1988.
10. S. Shi and H. Rabitz, "Optimal control of bond-selectivity in unimolecular reactions," Comp. Phys. Commun., vol.63, p. 71, 1991.
11. S. E. Sklarz, D. J. Tannor, and N. Khaneja, "Optimal control of quantum dissipative dynamics: Analytic solution for cooling the three-level A system," Phy. Rev. A, vol.69, p. 053408, 2004.
12. W. Jakubetz and J. Manz, "Theory of optimal laser pulses for selective transitions between molecular eigenstates," Chem. Phys. Lett., vol.165, p. 100, 1990.
13. H. Shen, J. P. Dussault, and A. D. Bandrauk, "Optimal pulse shaping for coherent control by the penalty algorithm," Chem. Phys. Lett., vol.221, p. 498, 1994.
14. Y. J.Yan, R. E. Gillilan, R. M. Whitnell, K. R.Wilson, and S. Mukamel, "Optical control of molecular dynamics: Liouville-space theory," J. Phys. Chem., vol.97, p. 2320, 1993.
15. N. Khaneja, R. Brockett, and S. J. Glaser, "Time optimal control in spin systems," Phys. Rev. A, vol.63, p. 032308, 2001.
16. H.Yuan and N. Khaneja, "Reachable set of bilinear control system with time varying drift," Syst. Control Lett., vol.55/6, pp. 501-507, 2006.
17. H.Yuan and N. Khaneja, "Time optimal control of coupled qubits under nonstationary interactions," Phys. Rev. A, vol.72, p. 040301, 2005.
18. H. Yuan, S. Glaser, and N. Khaneja, "Geodesics for efficient creation and propagation of order along Ising spin chains," Phys. Rev. A, vol.76, p. 012316, 2007.
19. H. Yuan, R. Zeier, and N. Khaneja, "Elliptic functions and efficient control of Ising spin chains with unequal couplings," Phys. Rev. A, vol.77, p. 032340, 2008.
20. T. Hornung, S. Gordienko, R. de Vivie-Riedle, and B. Verhaar, "Optimal conversion of an atomic to a molecular Bose-Einstein condensate," Phys. Rev. A, vol.66, p. 043607, 2002.
21. S. E. Sklarz and D. J. Tannor, "Loading a Bose-Einstein condensate onto an optical lattice: An application of optimal control theory to the nonlinear Schrödinger equation," Phys. Rev. A, vol.66, p. 053619, 2002.
22. S. E. Sklarz, I. Friedler, D. J. Tannor, Y. B. Band, and C. J. Williams, "Flat-phase loading of a Bose-Einstein condensate into an optical lattice," Phys. Rev. A, vol.66, p. 053620, 2002.
23. C. Rangan and P. H. Bucksbaum, "Optimally shaped terahertz pulses for phase retrieval in a Rydgerg-atom data register," Phys. Rev. A, vol.64, p. 033417, 2001.
24. C. M. Tesch, L. Kurtz, and R. de Vivie-Riedle, "Applying optimal control theory for elements of quantum computation in molecular systems," Chem. Phys. Lett., vol.343, p. 633, 2001.
25. J. P. Palao and R. Kosloff, "Quantum computing by an optimal control algorithm for unitary transformations," Phys. Rev. Lett., vol.89, p. 188301, 2002.
26. H. Yuan, R. Zeier, N. Khaneja, and S. Lloyd, "Constructing two-qubit gates with minimal couplings," Phys. Rev. A, vol.79, p. 042309, 2009.
27. N. Khaneja et al., "Shortest paths for efficient control of indirectly coupled qubits," Phys. Rev. A, vol.75, p. 012322, 2007.
28. M. Leibscher, I. S. Averbukh, and H. Rabitz, "Molecular alignment by trains of short laser pulses," Phys. Rev. Lett., vol.90, p. 213001, 2003.
29. H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, "Whither the future of controlling quantum phenomena?," Science, vol.288, p. 824, 2000.
30. R. J. Gordon and S. A. Rice, "Active control of the dynamics of atoms and molecules," Annu. Rev. Phys. Chem., vol.48, p. 601, 1997.
31. A. Bartana, R. Kosloff, and D. J. Tannor, "Laser cooling of molecular internal degrees of freedom by a series of shaped pulses," J. Chem. Phys., vol.99, p. 196, 1993.
32. A. Bartana, R. Kosloff, and D. J. Tannor, "Laser cooling of internal degrees of freedom II," J. Chem. Phys., vol.106, p. 1435, 1997.
33. D. J. Tannor and A. Bartana, "On the interplay of control fields and spontaneous emission in laser cooling," J. Phys. Chem. A., vol.103, p. 10359, 1999.
34. J. S. Cao, M. Messina, and K. R.Wilson, "Quantum control of dissipative systems: Exact solutions," J. Chem. Phys., vol.106, p. 5239, 1997.
35. P. Gross and S. D. Schwartz, "External field control of condensed phase reactions," J. Chem. Phys., vol.109, p. 4843, 1998.
36. Y. Ohtsuki, K. Nakagami, W. Zhu, and H. Rabitz, "Quantum optimal control of wave packet dynamics under the influence of dissipation," Chem. Phys., vol.287, p. 197, 2003.
37. N. Khaneja, T. Reiss, B. Luy, and S. J. Glaser, "Optimal control of spin dynamics in the presence of relaxation," J. Magn. Reson., vol.162, p. 311, 2003.
38. G. Lindblad, "Entropy, information and quantum measurements," Commun. Math. Phys., vol.33, p. 305, 1973.
39. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, "Completely positive dynamical semigroups of N-level systems," J. Math. Phys, vol.17, p. 821, 1976.
40. R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications. New York: Springer, 1986.
41. D. Bacon, A. M. Childs, I. L. Chuang, J. Kempe1,5,6, D. W. Leung, and X. Zhou, "Universal simulation of Markovian quantum dynamics," Phys. Rev. A., vol.64, p. 062302, 2001.
42. R. Bhatia, Matrix Analysis. New York: Springer, 1997.
43. K. Kraus, States, Effects and Operations: Fundamental Notions of Quantum Theory. Berlin, Germany: Springer, 1983.
44. A. Uhlmann, "Sätze über Dichtematrizen," Math.-Naturwiss. Reihe, vol.20, p. 633, 1971.