Year: 2026
Type: preprint
Abstract: We determine when qubit controls admit an effective generator that drives every initial state to the same pure state. Lie wedges enforce nonnegative weights for dissipative generators and thereby preserve the distinction between reversible control and irreversible dissipation lost under Lie-algebra closure. For drift-free qubits with Hamiltonian controls available with either sign and at most one independently actuated dissipator generated by a traceless jump operator, we classify all nontrivial systems into thirteen structural strata. Explicit tests using the control algebra and channel data assign each system to a stratum. Necessary and sufficient conditions determine whether its Lie wedge contains a stabilizing generator and, when it does, the minimum number of control-rotated dissipative orientations required. These conditions distinguish stabilizable and non-stabilizable systems even when they share the same generated Lie algebra and stratum. In an exceptional stratum, one dissipative orientation is insufficient even with the available Hamiltonian controls, whereas averaging two orientations of the same channel produces a stabilizing generator.
Source: arXiv (Cornell University)
Author: Wang, Yibin
Institution: Nagoya University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216066037