Entanglement-breaking superchannels
Entanglement-breaking superchannels
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DOI：
10.22331/q-2020-07-16-299
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发表时间：
2019-10
期刊：
影响因子：
6.4
通讯作者：
Senrui Chen;E. Chitambar
中科院分区：
文献类型：
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作者：
Senrui Chen;E. Chitambar
在本文中，我们启动了纠缠破坏（EB）超级通道的研究。当作用于二部完全正（CP）图的一侧时，这些过程总是产生可分离的图。 EB 超级通道是众所周知的 EB 通道的概括。我们给出了 EB 超级图和超级通道的几个等效特征。与对应的通道不同，我们发现并非每个 EB 超级通道都可以实现为测量和准备超级通道。我们还证明许多 EB 超级通道可以被超级激活，因为它们在串联时可以输出不可分离的通道。然后，我们介绍超级通道的 CPTP 和 CP 完整图像的概念，它们分别捕获确定性和概率性通道可转换性。这使我们能够表征 EB 超级通道在不同场景下生成 CP 地图的能力，并揭示了通道和超级通道之间的一些根本区别。最后，我们放宽可分离通道的定义以包括 (p,q)-非纠缠通道，它们是不能使用 p 维和 q 维辅助系统产生纠缠的二分通道。通过引入和研究 k-EB 图，我们构建了未完全打破纠缠的 (p,q)-EB 超级通道的示例。还提供了 (p,q)-EB 超级通道表征的部分结果。
In this paper we initiate the study of entanglement-breaking (EB) superchannels. These are processes that always yield separable maps when acting on one side of a bipartite completely positive (CP) map. EB superchannels are a generalization of the well-known EB channels. We give several equivalent characterizations of EB supermaps and superchannels. Unlike its channel counterpart, we find that not every EB superchannel can be implemented as a measure-and-prepare superchannel. We also demonstrate that many EB superchannels can be superactivated, in the sense that they can output non-separable channels when wired in series. We then introduce the notions of CPTP- and CP-complete images of a superchannel, which capture deterministic and probabilistic channel convertibility, respectively. This allows us to characterize the power of EB superchannels for generating CP maps in different scenarios, and it reveals some fundamental differences between channels and superchannels. Finally, we relax the definition of separable channels to include (p,q)-non-entangling channels, which are bipartite channels that cannot generate entanglement using p- and q-dimensional ancillary systems. By introducing and investigating k-EB maps, we construct examples of (p,q)-EB superchannels that are not fully entanglement breaking. Partial results on the characterization of (p,q)-EB superchannels are also provided.