Extending additivity from symmetric to asymmetric channels

Entropy Uncertainty Relations and Strong Sub-additivity of Quantum Channels

We prove an entropic uncertainty relation for two quantum channels, extending the work of Frank and Lieb for quantum measurements. This is obtained via a generalized strong super-additivity (SSA) of quantum entropy. Motivated by Petz's algebraic SSA inequality, we also obtain a generalized SSA for quantum relative entropy. As a special case, it gives an improved data processing inequality.

Remarks on additivity of the Holevo channel capacity and of the entanglement of formation

The purpose of these notes is to discuss the relation between the additivity questions regarding the quantities (Holevo) capacity of a quantum channel T and entanglement of formation of a given bipartite state. In particular, using the Stinespring dilation theorem, we give a formula for the channel capacity involving entanglement of formation. This can be used to show that additivity of the latter for some states can be inferred from the additivity of capacity for certain channels. We demonstrate this connection for a family of group--covariant channels, allowing us to calculate the entangleme…

从置换对称性到通信界与可加性

From Permutation Symmetry to Communication Bounds and Additivity

本文证明完全置换不变性限制量子信道通信优势，使渐近优化简化为单次使用，并建立强逆定理与输出熵界，揭示可加性结果的统一结构。

一个完全高斯的量子 Stein 引理

A fully Gaussian quantum Stein's lemma

该研究针对受限集体高斯测量下的多模玻色子高斯态，建立了 Stein 指数的单字母公式，揭示第一、第二矩的渐近解耦，并排除中心高斯态下集体测量的优势。

Maximal output purity and capacity for asymmetric unital qudit channels

We consider generalizations of depolarizing channels to maps in which the identity channel is replaced by a convex combinations of unitary conjugations. We show that one can construct unital channels of this type for which the input which achieves maximal output purity is unique. We give conditions under which multiplicativity of the maximal p-norm and additivity of the minimal output entropy. We also show that the Holevo capacity need not equal log d - the minimal entropy as one might expect for a convex combination of unitary conjugations. Conversely, we give examples for which this conditio…

量子通道保持σ-可加性和乌拉姆可测基数

Quantum channels preserving sigma-additivity on diagonal von Neumann algebras and Ulam measurable cardinals

研究量子态在$\ell_2(κ)$上的性质与基数$κ$的集合论性质之间的相互作用，探讨σ-可加态的存在性及其结构动力学特性，证明对角代数上的σ-可加态可表示为皮蒂积分，构建量子通道将正常态映射到σ-可加态。