Lie-Semigroup Structures for Reachability and Control of Open Quantum Systems: Viewing Markovian Quantum Channels as Lie Semigroups and GKS-Lindblad Generators as Lie Wedge
G. Dirr, U. Helmke, I. Kurniawan, T. Schulte-Herbrueggen
备注：
As accepted for "Reports on Mathematical Physics": includes new section relating divisibility of semigroups to Markovian quantum channels; 17 pages, 2 figures
In view of controlling finite dimensional open quantum systems, we provide a unified Lie-semigroup framework describing the structure of completely positive trace-preserving maps. It allows (i) to identify the Kossakowski-Lindblad generators as the Lie wedge of a subsemigroup, (ii) to link properties of Lie semigroups such as divisibility with Markov properties of quantum channels, and (iii) to characterise reachable sets and controllability in open systems. We elucidate when time-optimal controls derived for the analogous closed system already give good fidelities in open systems and when a more detailed knowledge of the open system (e.g., in terms of the parameters of its Kossakowski-Lindblad master equation) is actually required for state-of-the-art optimal-control algorithms. -- As an outlook, we sketch the structure of a new, potentially more efficient numerical approach explicitly making use of the corresponding Lie wedge.
Gorini-Kossakowski-Sudarshan-Lindblad equation in different bases: application to driven-dissipative two- and multilevel systems
B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine（乌克兰国家科学院B.维尔金低温物理与工程研究所）；Center for Quantum Computing, RIKEN（理化学院量子计算中心）；V. N. Karazin Kharkiv National University（V.N.卡拉津哈尔科夫国立大学）；Department of Mathematics, Kyiv School of Economics（基辅经济学院数学系）
Possibility of the total thermodynamic entropy production rate of a finite-sized isolated quantum system to be negative for the Gorini-Kossakowski-Sudarshan-Lindblad-type Markovian dynamics of its subsystem
A Fractional Calculus Framework for Open Quantum Dynamics: From Liouville to Lindblad to Memory Kernels
Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory（太平洋西北国家实验室物理与计算科学部）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）
Path-Integral Formulation of Bosonic Markovian Open Quantum Dynamics with Monte Carlo stochastic trajectories using the Glauber-Sudarshan P, Wigner, and Husimi Q Functions and Hybrids
