标题： 林德布拉德算符与后选择非厄米拓扑 显示英文标题

标题： Lindbladian versus Postselected Non-Hermitian Topology

摘要： 非厄米“哈密顿量”的最新拓扑分类通常被解释为随时间衰减或增长的纯量子态。 然而，具有损耗和增益的多体系统通常更适合用混合态开放量子动力学来描述，这仅在对测量结果进行后选择时对应于纯态非厄米动力学。 由于后选择随着粒子数的增加而呈指数级成本，我们在此研究非厄米拓扑最重要的例子在没有后选择的情况下能存活到什么程度：即一维空间中非厄米皮肤效应及其与体缠绕数的关系。 在定义二次费米子系统的林德布拉德超算符的缠绕数之后，我们系统地将其与相关后选择非厄米哈密顿量的缠绕数联系起来。 我们证明，在没有增益（损耗）的情况下，这两个缠绕数相等（相反），并对此关系提供了物理解释。 当同时存在损耗和增益时，林德布拉德缠绕数通常保持量化且不为零，尽管在分隔损耗和增益主导区域的相变点上它可以改变符号。 这种导致林德布拉德皮肤效应局域化反转的相变被后选择所掩盖。 我们还发现了一种情况，去除后选择会从原本拓扑平凡的非厄米动力学中诱导出皮肤效应。 显示英文摘要

摘要： The recent topological classification of non-Hermitian `Hamiltonians' is usually interpreted in terms of pure quantum states that decay or grow with time. However, many-body systems with loss and gain are typically better described by mixed-state open quantum dynamics, which only correspond to pure-state non-Hermitian dynamics upon a postselection of measurement outcomes. Since postselection becomes exponentially costly with particle number, we here investigate to what extent the most important example of non-Hermitian topology can survive without it: the non-Hermitian skin effect and its relationship to a bulk winding number in one spatial dimension. After defining the winding number of the Lindbladian superoperator for a quadratic fermion system, we systematically relate it to the winding number of the associated postselected non-Hermitian Hamiltonian. We prove that the two winding numbers are equal (opposite) in the absence of gain (loss), and provide a physical explanation for this relationship. When both loss and gain are present, the Lindbladian winding number typically remains quantized and non-zero, though it can change sign at a phase transition separating the loss and gain-dominated regimes. This transition, which leads to a reversal of the Lindbladian skin effect localization, is rendered invisible by postselection. We also identify a case where removing postselection induces a skin effect from otherwise topologically trivial non-Hermitian dynamics.