S G Schirmer et al 2002 J. Phys. A: Math. Gen. 35 8551 doi:10.1088/0305-4470/35/40/313
S G Schirmer1, A I Solomon1 and J V Leahy2
Show affiliationsWe address the question of which quantum states can be inter-converted under the action of a time-dependent Hamiltonian. In particular, we consider the problem as applied to mixed states, and investigate the difference between pure- and mixed-state controllabilities introduced in previous work. We provide a complete characterization of the eigenvalue spectrum for which the state is controllable under the action of the symplectic group. We also address the problem of which states can be prepared if the dynamical Lie group is not sufficiently large to allow the system to be controllable.
15A90 Applications of matrix theory to physics
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
Issue 40 (11 October 2002)
Received 25 January 2002, in final form 22 March 2002
Published 24 September 2002
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