标题： 一般开放量子系统的映射及线性量子误差校正理论 显示英文标题

标题： Maps for general open quantum systems and a theory of linear quantum error correction

摘要： 我们证明，无论初始总系统状态的形式如何，一个开放量子系统的量子次动力学总是可以用一个厄米特映射来描述。由于量子误差校正理论是基于完全正（CP）映射的假设而发展起来的，我们提出了一种广义的线性量子误差校正理论，该理论适用于描述开系统演化的任何线性映射。在厄米特映射这一在物理上相关的场景下，我们表明基于CP映射的量子误差校正理论无需修改即可应用。然而，我们还表明，还存在一种更普遍的情况，即恢复映射是厄米特但不是CP的。由于非CP映射在其取值范围内具有非正定矩阵，我们提供了通用线性映射的正定域的几何特征描述。特别是，我们表明这个域是凸的，并且这意味着可以简单地找到其边界的算法。 显示英文摘要

摘要： We show that quantum subdynamics of an open quantum system can always be described by a Hermitian map, irrespective of the form of the initial total system state. Since the theory of quantum error correction was developed based on the assumption of completely positive (CP) maps, we present a generalized theory of linear quantum error correction, which applies to any linear map describing the open system evolution. In the physically relevant setting of Hermitian maps, we show that the CP-map based version of quantum error correction theory applies without modifications. However, we show that a more general scenario is also possible, where the recovery map is Hermitian but not CP. Since non-CP maps have non-positive matrices in their range, we provide a geometric characterization of the positivity domain of general linear maps. In particular, we show that this domain is convex, and that this implies a simple algorithm for finding its boundary.