A longstanding tool to characterize the evolution of open Markovian quantum systems is the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation. However, in some cases, open quantum systems can be effectively described with non-Hermitian Hamiltonians, which have attracted great interest in the last twenty years due to a number of unconventional properties, such as the appearance of exceptional points. Here, we present a short review of these two different approaches aiming in particular to highlight their relation and illustrate different ways of connecting non-Hermitian Hamiltonian to a GKSL master equation for the full density matrix.

GKSL（Gorini-Kossakowski-Sudarshan-Lindblad）主方程是表征开放马尔可夫量子系统演化的长期工具。然而，在某些情况下，开放量子系统可以用非厄米哈密顿量有效地描述，由于一些非常规的性质，例如异常点的出现，在过去的二十年中引起了极大的兴趣。在这里，我们简要回顾了这两种不同的方法，特别是强调它们的关系，并说明将非厄米哈密顿量与全密度矩阵的 GKSL 主方程联系起来的不同方法。