Recovering Complete Positivity of Non-Markovian Quantum Dynamics with Choi-Proximity Regularization,Physical Review X

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Recovering Complete Positivity of Non-Markovian Quantum Dynamics with Choi-Proximity Regularization
Physical Review X ( IF 11.6 ) Pub Date : 2024-07-17 , DOI: 10.1103/physrevx.14.031010
Antonio D’Abbruzzo ₁ , Donato Farina _{2,

3} , Vittorio Giovannetti ₁

Affiliation

A relevant problem in the theory of open quantum systems is the lack of complete positivity of dynamical maps obtained after weak-coupling approximations, a famous example being the Redfield master equation. A number of approaches exist to recover well-defined evolutions under additional Markovian assumptions, but much less is known beyond this regime. Here, we propose a numerical method to cure the complete-positivity violation issue while preserving the non-Markovian features of an arbitrary original dynamical map. The idea is to replace its unphysical Choi operator with its closest physical one, mimicking recent work on quantum process tomography. We also show that the regularized dynamics is more accurate in terms of reproducing the exact dynamics, which allows us to heuristically push the utilization of these master equations in moderate coupling regimes, where the loss of positivity can have a relevant impact.

中文翻译：

使用 Choi-Proximity 正则化恢复非马尔可夫量子动力学的完全正性

开放量子系统理论中的一个相关问题是在弱耦合近似后获得的动力学映射缺乏完全正性，一个著名的例子是 Redfield 主方程。在额外的马尔可夫假设下，有许多方法可以恢复定义明确的进化，但在这个机制之外了解的要少得多。在这里，我们提出了一种数值方法来解决完全正性违规问题，同时保留任意原始动力学映射的非马尔可夫特征。这个想法是用最接近的物理 Choi 算子替换其非物理的 Choi 算子，模仿最近关于量子过程断层扫描的工作。我们还表明，正则化动力学在再现精确动力学方面更加准确，这使我们能够启发式地推动这些主方程在中等耦合状态下的使用，其中正性的损失可能会产生相关影响。

更新日期：2024-07-17

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