The solutions to the celebrated Kossakowski-Lindblad equation extended by coherent controls yield Markovian quantum maps. More precisely, the set of all its solutions forms a semigroup of completely positive trace-preserving maps taking the specific form of a Lie semigroup. Non-trivial symmetries of these semigroups are shown to preclude accessibility in Markovian dissipative systems. This is the open-system analogue to closed systems, where triviality of (quadratic) symmetries of the Hamiltonian part suffices to decide that the system is fully controllable. The findings are placed into a unifying Lie frame of quantum systems and control theory alongside with illustrating examples.

中文翻译：

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从 Kossakowski-Lindblad 李半群看量子系统理论——反之亦然

由相干控制扩展的著名 Kossakowski-Lindblad 方程的解产生马尔可夫量子图。更准确地说，它的所有解的集合形成了一个完全正迹保留映射的半群，采用李半群的特定形式。这些半群的非平凡对称性被证明排除了马尔可夫耗散系统的可访问性。这是封闭系统的开放系统模拟，其中哈密顿部分的（二次）对称性的琐碎性足以决定系统是完全可控的。这些发现与说明性示例一起被放入量子系统和控制理论的统一李框架中。