How fast can a quantum state evolve into a target state?

Physica D: Nonlinear Phenomena

Volumn 189, Issue 1-2, 2004, Pages 1-7

  Luo, Shunlong ^a,b  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

^b INSTITUT FÜR EXPERIMENTALPHYSIK   (Austria)

Author keywords

Evolution; Quantum search; Schr dinger dynamics; Time energy uncertainty relations; Transition probability

Indexed keywords

ALGORITHMS; ELECTRON TRANSITIONS; ELECTRONIC DENSITY OF STATES; HAMILTONIANS; NONLINEAR SYSTEMS;

QUANTUM SEARCH; TIME-ENERGY UNCERTAINTY RELATIONS;

QUANTUM THEORY;

EID: 0842265112     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2003.10.001     Document Type: Article

References (23)

1. Mandelstam L., Tamm I., The uncertainty relation between energy and time in nonrelativistic quantum mechanics. J. Phys. (Moscow). 9:1945;249-254.
2. Fleming G.N., A unitary bound on the evolution of nonstationary states. Nuovo Cimento A. 16:1973;232-240.
3. Bhattacharyya K., Quantum decay and Mandelstam-Tamm time energy inequality. J. Phys. A. 16:1983;2993-2996.
4. Home D., Whitaker M.A.B., Reflections on the quantum Zeno paradox. J. Phys. A. 19:1986;1847-1854.
5. Anandan J., Aharonov Y., Geometry of quantum evolution. Phys. Rev. Lett. 65:1990;1697-1700.
6. Vaidman L., Minimum time for the evolution to an orthogonal quantum state. Am. J. Phys. 60:1992;182-183.
7. Uffink J., The rate of evolution of quantum state. Am. J. Phys. 61:1993;935-936.
8. Pfeifer P., How fast can a quantum state change with time. Phys. Rev. Lett. 70:1993;3365-3368.
9. Vaidman L., Belkind O., Strict bounds on the Franson inequality. Phys. Rev. A. 57:1998;1583-1585.
10. Aharonov Y., Massar S., Popescu S., Measuring energy, estimating Hamiltonian, and the time-energy uncertainty relation. Phys. Rev. A. 66:2002;052107.
11. Margolus N., Levitin L.B., The maximum speed of dynamical evolution. Physica D. 120:1998;188-195.
12. Lloyd S., Ultimate physical limits to computation. Nature. 406:2000;1047-1054.
13. Lloyd S., Computational capacity of the universe. Phys. Rev. Lett. 88:2002;237901.
14. Luo S.L., Wang Z., Zhang Q., An inequality for characteristic functions and its applications to uncertainty relations and the quantum Zeno effect. J. Phys. A. 35:2002;5935-5941.
15. Misra B., Sudarshan E.C.G., The Zeno's paradox in quantum theory. J. Math. Phys. 18:1977;756-763.
16. Chiu C.B., Sudarshan E.C.G., Misra B., Time evolution of unstable quantum states and a resolution of Zeno's paradox. Phys. Rev. D. 16:1977;520-529.
17. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.
18. Weinacht T.C., Ahn J., Bucksbaum P.H., Controlling the shape of a quantum wavefunction. Nature. 397:1999;233-235.
19. Rabitz H., de Vivie-Riedle R., Motzkus M., Kompa K., Whither the future of controlling quantum phenomena. Science. 288:2000;824-828.
20. Khaneja N., Brockett R., Glaser S.J., Time optimal control in spin system. Phys. Rev. A. 63:2001;032308.
21. Farhi E., Gutmann S., Analog analogue of a digital quantum computation. Phys. Rev. A. 57:1998;2403-2405.
22. Grover L.K., Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 78:1997;325-328.
23. A. Messiah, Quantum Mechanics, vol. I, North-Holland, Amsterdam, 1976, p. 320.