Capacities of quantum channels and decoherence times both quantify the extent to which quantum information can withstand degradation by interactions with its environment. However, calculating capacities directly is known to be intractable in general. Much recent work has focused on upper bounding certain capacities in terms of more tractable quantities such as specific norms from operator theory. In the meantime, there has also been substantial recent progress on estimating decoherence times with techniques from analysis and geometry, even though many hard questions remain open. In this article, we introduce a class of continuous-time quantum channels that we called transferred channels , which are built through representation theory from a classical Markov kernel defined on a compact group. In particular, we study two subclasses of such kernels: Hörmander systems on compact Lie-groups and Markov chains on finite groups. Examples of transferred channels include the depolarizing channel, the dephasing channel, and collective decoherence channels acting on $d$ qubits. Some of the estimates presented are new, such as those for channels that randomly swap subsystems. We then extend tools developed in earlier work by Gao, Junge and LaRacuente to transfer estimates of the classical Markov kernel to the transferred channels and study in this way different non-commutative functional inequalities. The main contribution of this article is the application of this transference principle to the estimation of decoherence time, of private and quantum capacities, of entanglement-assisted classical capacities as well as estimation of entanglement breaking times, defined as the first time for which the channel becomes entanglement breaking. Moreover, our estimates hold for non-ergodic channels such as the collective decoherence channels, an important scenario that has been overlooked so far because of a lack of techniques.

中文翻译：

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估计马尔可夫半群退相干时间和容量的群转移技术

量子通道的容量和退相干时间都可以量化量子信息通过与环境相互作用而可以承受的降解程度。但是，直接计算容量通常很难解决。最近的许多工作都集中在以更易处理的数量为上限的某些容量上，例如操作员理论中的特定规范。同时，尽管仍然存在许多难题，但利用分析和几何技术估算去相干时间也取得了实质性进展。在本文中，我们介绍了一类连续时间量子通道，我们称之为转移渠道 ，是通过表示理论从紧凑组上定义的经典马尔可夫核构建的。特别是，我们研究了此类内核的两个子类：紧凑李群上的Hörmander系统和有限群上的马尔可夫链。传输通道的示例包括去极化通道，相移通道和作用在其上的集体去相干通道 $ d $ 量子比特。提出的一些估计是新的，例如那些随机交换子系统的信道的估计。然后，我们扩展由Gao，Junge和LaRacuente在早期工作中开发的工具，以将经典马尔可夫核的估计值转移到转移的通道中，并以此方式研究不同的非交换功能不等式。本文的主要贡献是将该转移原理应用于退相干时间，私有和量子容量，纠缠辅助经典容量的估计以及纠缠破坏时间的估计，定义为通道的首次变得纠缠不清。此外，我们的估算适用于非遍历渠道，例如集体去相干渠道，