因为实际系统难以避免的与外界环境进行着物质、能量交换，所以对量子开放系统的研究在理论和实验上都有重要意义。由于和外界环境的相互作用，量子开放系统的动力学更加丰富。同时，量子开放系统有不同的描述方式：当其环境满足马尔可夫近似时，其动力学可以用Lindbald方程描述；当环境不满足马尔可夫近似时，可以通过约化掉总系统中环境的自由度来研究开放系统的性质；有增益和损耗的开放系统也可以用非厄米哈密顿量描述。本论文介绍了四部分内容：用Lindblad方程描述的量子开放系统的Lindbald谱的结构及熵的动力学；用推广的Lindabld方程来描述带有量子测量的演化过程以及其中的纠缠熵相变；非厄米系统中的纠缠熵相变、边界效应；一般的开放系统的纠缠谱的简并性质。对于环境满足马尔科夫近似的可以用Lindblad方程描述的开放系统，其熵的动力学的时间尺度由什么决定？我们利用二阶Renyi 熵的动力学与Lindblad谱之间的近似关系，将熵的动力学和Lindblad谱的结构直接联系起来。以强耗散情况为例，我们发现开放系统的Lindblad谱有分隔的结构，且有两种不同能量尺度，这两种能量尺度分别决定了二阶Renyi熵的短时和长时动力学，导致其短时和长时相反的行为。同时，利用Lindblad谱，我们也自然地把能谱结构因子、Loschmidt echo推广到开放系统中，这帮助我们分析开放系统动力学的普适行为。当环境和开放系统的相互作用可以描述为对开放系统进行测量时，如何得到描述带有量子测量的开放系统的动力学的微分方程？我们发现可以用推广的Lindblad方程描述由测量引起的纠缠熵相变中的R\‘enyi熵的动力学，其也体现了后选择在有测量的演化中的重要作用。对于一般的非厄米项来源于测量的非厄米系统，我们提出可以用全计数统计来探测其中的纠缠熵相变，这对在实验中观测到纠缠熵相变提供了一种可能；同时，我们通过时空对偶性将非厄米系统的内部对边界条件的敏感性和封闭量子混沌系统对初始时间的敏感性联系起来，这使得对有相互作用的非厄米系统的边界效应的讨论更进了一步。 对于环境不满足马尔科夫近似的开放系统，我们研究了其与环境间的纠缠谱。我们通过纠缠谱把封闭系统的Lieb-Schulz-Mattis (LSM) 定理推广到开放系统：当一个满足LSM限制的开放系统是短程关联时，其纠缠谱不能有非简并、有能隙的最小值。与最初的封闭系统的LSM定理所表示的UV-IR对应相比，我们的推广揭示了紫外数据和拓扑约束也与量子开放系统中的纠缠有重要联系。

Because actual systems inevitably exchange matter and energy with the external environment, the study of quantum open systems is of great significance both theoretically and experimentally. The dynamics of quantum open systems are richer due to interactions with the external environment. Quantum open systems can be described in different ways. When its environment satisfies the Markov approximation, its dynamics can be described by the Lindbald equation; when the environment does not satisfy the Markov approximation, it can be studied by reducing the degrees of freedom of the environment in the total system that interacts with the environment; open systems with gains and losses can also be described by non-Hermitian Hamiltonians.This paper introduces four parts: the structure of the Lindblad spectrum and its entropy dynamics of quantum open systems described by the Lindblad equation; the use of the generalized Lindblad equation to describe the evolution process involving quantum measurement, and the measurement-induced entanglement phase transition in it; the degeneracy properties of the entanglement spectrum of general open systems that interact with the environment, and entanglement phase transition and boundary effects in non-Hermitian systems.For an open system whose environment satisfies the Markov approximation and can be described by the Lindblad equation, what determines the time scale of its entropy dynamics? We use the approximate relationship between the dynamics of second-R\‘enyi entropy and the Lindblad spectrum to directly connect the entropy dynamics and the structure of the Lindblad spectrum. Taking the case of strong dissipation as an example, we found that the Lindblad spectrum of the open system has a segmented structure and has two different energy scales. These two energy scales determine the short-time and long-time dynamics of the second-R\‘enyi entropy respectively, leading to its short-time and long-time opposite behaviors. Also, using the Lindblad spectrum, we can naturally extend the spectrum form factor and Loschmidt echo to open systems, which helps us analyze the universal behavior of open system dynamics.How to get differential equations that describe the dynamics of an open system with quantum measurements, when the interaction of the environment and the open system can be described as measurements of the open system? We find that the generalized Lindblad equation can be used to describe the dynamics of R\‘enyi entropy in the measurement-induced entanglement phase transition, and this equation also reflects the important role of post-selection in the evolution with measurement.For general non-Hermitian systems where the non-Hermitian terms are derived from measurements, we propose that the measurement-induced phase transition can be detected through the full counting statistics, which provides a possibility for observing this phase transition in experiments. Also, for the sensitivity of the bulk of non-Hermitian systems to boundary conditions, we use spacetime dual to connect its sensitivity to boundary conditions and the sensitivity of closed quantum chaotic systems to initial time conditions, which makes the discussion of boundary effects in interacting non-Hermitian systems goes one step further.For an open system whose environment does not satisfy the Markov approximation, we study the entanglement spectrum between it and the environment. We extend the Lieb-Schulz-Mattis (LSM) theorem in closed systems to open systems through the entanglement spectrum: when an open system that satisfies the LSM constraints is short-range correlated, its entanglement spectrum cannot have a gapped non-degenerate minimum. Compared with the UV-IR correspondence represented by the original LSM theorem, our generalization reveals that UV data and topological constraints are also significantly related to entanglement properties in open quantum systems.