On the Lyapunov-Perron reducible Markovian Master Equation

Completely Reducible maps in Quantum Information Theory

In order to compute the Schmidt decomposition of $A\in M_k\otimes M_m$, we must consider an associated self-adjoint map. Here, we show that if $A$ is positive under partial transposition (PPT) or symmetric with positive coefficients (SPC) or invariant under realignment then its associated self-adjoint map is completely reducible. We give applications of this fact in Quantum Information Theory. We recover some theorems recently proved for PPT and SPC matrices and we prove these theorems for matrices invariant under realignment using theorems of Perron-Frobenius theory. We also provide a new pro…

关于ergodic量子过程的可约性理论与ergodic定理

Reducibility Theory and Ergodic Theorems for Ergodic Quantum Processes

本文发展了一种类似于Perron-Frobenius理论的框架，用于研究由平稳和ergodic随机过程采样出的有限维矩阵代数上的随机量子通道乘积，统一了多种模型，包括i.i.d.、马尔可夫、周期性和准周期性模型，并给出了i.i.d.情况下的理论改进。

马尔可夫量子动力学的戴维斯不可约性准则

Criteria for Davies Irreducibility of Markovian Quantum Dynamics

本文提出马尔可夫量子动力学戴维斯不可约性的代数准则，结合实例分析可约性的调控，厘清戴维斯与埃文斯可约性的差异，并探讨纯态稳定化相关问题。