发表机构
Graduate School of Mathematics, Nagoya University（名古屋大学数学研究科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过李楔分层将单通道量子比特控制分为十三类，并据此判定纯态可镇定性，揭示李代数遗漏的控制能力。
AI 中文摘要
李代数描述了控制生成元的组合方式，但在开放系统中，它们抹去了可逆控制与不可逆耗散之间的区别。李楔保留了这一信息。我们研究无漂移单量子比特系统，该系统具有双向哈密顿控制，以及至多一个由无迹跳跃算子生成的独立驱动耗散器。在本工作中，我们证明这些系统可分为由生成代数及其李楔几何定义的十三个结构层。控制代数和四个通道性质决定层；在每个楔中，可逆方向恰好是相干控制。然后，我们利用分层来确定楔是否包含具有唯一全局吸引纯态的生成元。在五个层中，可镇定性取决于额外的通道数据。在一个特殊层中，没有单一的控制旋转耗散方向足够，但对楔中两个这样的方向取平均可实现镇定。因此，李楔揭示了生成李代数所遗漏的控制能力。
英文摘要
We ask when qubit controls can produce an effective generator that drives every initial state to the same pure state. Lie-algebra closure alone cannot answer this question because it loses the distinction between reversible control and irreversible dissipation. Lie wedges retain this distinction by enforcing nonnegative strengths for dissipative generators. 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 types, or strata. Explicit tests assign each system to a stratum, and necessary and sufficient conditions determine whether its Lie wedge contains a stabilizing generator. These criteria distinguish stabilizable and non-stabilizable systems even when they share the same generated Lie algebra and stratum. In one exceptional stratum, a single dissipative orientation cannot stabilize a pure state even with the available Hamiltonian controls. Averaging two orientations of the same dissipative channel, related by those controls, produces a stabilizing generator.
Comments29 pages, 1 figure. Revised title and abstract; added worked examples and an explicit convergence bound; reorganized proofs into appendices
