李布拉德ians能走多远？
How Far do Lindbladians Go?
AI总结：
研究了开放量子系统在马尔可夫控制模型下的可控性，探讨了最少耗散对状态空间传递性的影响及几何障碍。
AI中文摘要：
我们研究了在一般马尔可夫控制模型下，有限维开放量子系统可控性的问题，该模型结合了完整的相干（幺正）控制与可调耗散通道。假设哈密顿量控制是一个生成su(n)的霍尔曼德系统，我们问最少的耗散是否足以使整个状态空间D(H)可控。我们证明了最小非单色噪声可以破坏幺正轨道不变量，并且在许多情况下，非常小的跃迁算子集可以对D(H)实现传递性。对于多量子比特系统，我们证明了对于自然资源如单量子比特振幅阻尼跃迁算子和退相位通道，有明确的传递性结果，并且当只有自共轭跃迁算子可用时（产生仅单色演化）会遇到障碍。我们进一步发展了一种几何观点，并提出了“提升”问题：当应用时间依赖的利布拉德ian到初始状态时，何时可以得到密度路径？为此，我们必须分析“角点流形”的切结构以及这种切结构如何反映利布拉德ian演化。在此框架基础上，我们推导了可达性标准和无法实现的结果，基于规范减少对齐条件，包括由于允许的切方向与耗散收缩不兼容而产生的几何障碍。
英文摘要：
We study controllability of finite-dimensional open quantum systems under a general Markovian control model combining full coherent (unitary) control with tunable dissipative channels. Assuming the Hamiltonian controls is a Hörmander system that generate $\mathfrak{su}(n)$, we ask how little dissipation suffices to make the full state space $\mathcal{D}(\mathcal{H})$ controllable. We show that minimal non-unital noise can break unitary-orbit invariants and, in many cases, a very small set of jump operators yields transitivity on $\mathcal{D}(\mathcal{H})$. For multi-qubit systems we prove explicit transitivity results for natural resources such as a single-qubit amplitude-damping jump together with a dephasing channel, and we identify obstructions when only self-adjoint jump operators are available (yielding only unital evolutions). We further develop a geometric viewpoint and ask the ``lifting'' question: when can a path of densities be obtained from applying a time-dependent family of Lindbladian to an initial state? For this, we have to analyze the tangent structure of the ``manifold with corners'' and how this tangent structure reflects Lindbldian evolution. Building on this framework, we derive reachability criteria and no-go results based on a norm-decrease alignment condition, including a geometric obstruction arising from the incompatibility between admissible tangent directions and dissipative contraction.
