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Geometry and Response of Lindbladians

机译：Lindbladians的几何形状和响应

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Markovian reservoir engineering, in which time evolution of a quantum system is governed by a Lindblad master equation, is a powerful technique in studies of quantum phases of matter and quantum information. It can be used to drive a quantum system to a desired (unique) steady state, which can be an exotic phase of matter difficult to stabilize in nature. It can also be used to drive a system to a unitarily evolving subspace, which can be used to store, protect, and process quantum information. In this paper, we derive a formula for the map corresponding to asymptotic (infinite-time) Lindbladian evolution and use it to study several important features of the unique state and subspace cases. We quantify how subspaces retain information about initial states and show how to use Lindbladians to simulate any quantum channels. We show that the quantum information in all subspaces can be successfully manipulated by small Hamiltonian perturbations, jump operator perturbations, or adiabatic deformations. We provide a Lindblad-induced notion of distance between adiabatically connected subspaces. We derive a Kubo formula governing linear response of subspaces to time-dependent Hamiltonian perturbations and determine cases in which this formula reduces to a Hamiltonian-based Kubo formula. As an application, we show that (for gapped systems) the zero-frequency Hall conductivity is unaffected by many types of Markovian dissipation. Finally, we show that the energy scale governing leakage out of the subspaces, resulting from either Hamiltonian or jump-operator perturbations or corrections to adiabatic evolution, is different from the conventional Lindbladian dissipative gap and, in certain cases, is equivalent to the excitation gap of a related Hamiltonian.
机译：马尔科夫油藏工程是一个研究物质量子相和量子信息的有力技术，其中量子系统的时间演化由Lindblad主方程控制。它可用于将量子系统驱动到所需的（唯一）稳态，这可能是自然界中难以稳定的奇异物质阶段。它也可以用于将系统驱动到一个整体演化的子空间，该子空间可以用于存储，保护和处理量子信息。在本文中，我们推导了对应于渐近（无限时）Lindbladian演化的映射的公式，并用它来研究唯一状态和子空间情况的几个重要特征。我们量化子空间如何保留有关初始状态的信息，并展示如何使用Lindbladians模拟任何量子通道。我们表明，所有子空间中的量子信息都可以通过小的哈密顿扰动，跳跃算子扰动或绝热变形来成功操纵。我们提供了绝热连接的子空间之间的Lindblad诱导的距离概念。我们推导了一个Kubo公式，该公式控制子空间对时间相关的Hamilton扰动的线性响应，并确定该公式简化为基于Hamiltonian的Kubo公式的情况。作为一个应用，我们表明（对于有间隙的系统）零频率霍尔电导率不受许多类型的马尔可夫耗散的影响。最后，我们表明，由哈密顿量或跳跃算子的扰动或对绝热演化的修正所导致的控制子空间泄漏的能级不同于常规的林德布拉德耗散能隙，并且在某些情况下等于激励能隙相关的哈密顿量

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