Strong convergence of quantum channels: continuity of the Stinespring dilation and discontinuity of the unitary dilation
M. E. Shirokov
备注：
23 pages, in v6 the main results are strengthened essentially, in v5 section 6 devoted to application of the main results in quantum information theory is added, while sections 6-7 of v4 are replaced to a separate paper (arXiv:1802.05632)
We show that a sequence $\{Φ_n\}$ of quantum channels strongly converges to a quantum channel $Φ_0$ if and only if there exist a common environment for all the channels and a corresponding sequence $\{V_n\}$ of Stinespring isometries strongly converging to a Stinespring isometry $V_0$ of the channel $Φ_0$.
We also give a quantitative description of the above characterization of the strong convergence in terms of the appropriate metrics on the sets of quantum channels and Stinespring isometries. As a result, the uniform selective continuity of the complementary operation with respect to the strong convergence is established.
We show discontinuity of the unitary dilation by constructing a strongly converging sequence of channels which can not be represented as a reduction of a strongly converging sequence of unitary channels.
The Stinespring representation of strongly converging sequences of quantum channels allows to prove the lower semicontinuity of the entropic disturbance as a function of a pair (channel, input ensemble). Some corollaries of this property are considered.
Random Stinespring superchannel: converting channel queries into dilation isometry queries
Scuola Normale Superiore（比萨高等师范学院）；Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）；Inria, Télécom Paris – LTCI, Institut Polytechnique de Paris（法国国家信息与自动化研究所，巴黎理工学院-通信与图像实验室）
Quantum Channel Stein's Lemma with an Exponential Strong Converse
Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
Fock majorization in bosonic quantum channels with a passive environment
我们引入了一类称为被动环境玻色子信道的量子信道。从量子力学的观点来看，这些通道是相关的，因为它们对应于玻色子系统与处于被动状态的玻色子环境的能量保持线性耦合（通过使用幺正变换不能从其中提取能量），然后丢弃环境。在[New J. Phys. 18，073047（2016）]中定义的福克优序关系在这种情况下特别有用，因为与常规优序不同，它将状态的无序与其能量联系在一起。我们的主要结果是在所有被动环境玻色子通道的福克优化的保存。这意味着在被动状态的集合上的规则优化具有类似的保持属性，并且它还扩展到被动环境通道，其Stinespring膨胀涉及主动高斯酉。除了玻色子系统之外，引入的被动环境操作类自然地概括了热操作，并有望为量子系统的热力学提供新的见解。
