In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinite-dimensional open quantum dynamical systems following a unital Kossakowski–Lindblad master equation extended by controls. More precisely, their time evolution shall be governed by an inevitable potentially unbounded Hamiltonian drift term H0, finitely many bounded control Hamiltonians Hj allowing for (at least) piecewise constant control amplitudes [Formula: see text] plus a bang-bang (i.e., on-off) switchable noise term ГV in Kossakowski–Lindblad form. Generalizing standard majorization results from finite to infinite dimensions, we show that such bilinear quantum control systems allow to approximately reach any target state majorized by the initial one as up to now it only has been known in finite dimensional analogues. The proof of the result is currently limited to the bounded control Hamiltonians Hj and for noise terms ГV with compact normal V.

中文翻译：

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具有可切换 GKS–Lindblad 发生器的无限维单位开放量子系统的可达性

在量子系统理论中，一个基本问题归结为：给定一个初始状态，所讨论的动态系统可以达到哪些最终状态。在这里，我们考虑遵循由控制扩展的单位 Kossakowski-Lindblad 主方程的无限维开放量子动力系统。更准确地说，它们的时间演化应由不可避免的潜在无界哈密顿漂移项 H 控制0, 有限多有界控制哈密顿量 Hj允许（至少）分段恒定控制幅度 [公式：见文本] 加上一个 bang-bang（即开关）可切换噪声项 Г五Kossakowski-Lindblad 形式。将标准大化结果从有限维度推广到无限维度，我们表明，这种双线性量子控制系统允许近似地达到任何目标状态，因为到目前为止它只在有限维度类似物中才为人所知。结果的证明目前仅限于有界控制哈密顿量 Hj对于噪声项 Г五紧致法线 V。