C∗-extreme points of entanglement breaking maps

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Reviews in Mathematical Physics Pub Date : 2022-02-01 DOI:10.1142/S0129055X23500058

B. Bhat, Repana Devendra, N. Mallick, K. Sumesh

引用次数: 2

Abstract

In this paper, we study the [Formula: see text]-convex set of unital entanglement breaking (EB-)maps on matrix algebras. General properties and an abstract characterization of [Formula: see text]-extreme points are discussed. By establishing a Radon–Nikodym-type theorem for a class of EB-maps we give a complete description of the [Formula: see text]-extreme points. It is shown that a unital EB-map [Formula: see text] is [Formula: see text]-extreme if and only if it has Choi-rank equal to [Formula: see text]. Finally, as a direct consequence of the Holevo form of EB-maps, we derive a non-commutative analog of the Krein–Milman theorem for [Formula: see text]-convexity of the set of unital EB-maps.

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C * -纠缠断裂图的极值点

本文研究了矩阵代数上的单位纠缠破缺（EB-）映射的[公式：见正文]-凸集。讨论了[公式：见正文]-极值点的一般性质和抽象特征。通过建立一类EB映射的Radon–Nikodym型定理，我们给出了[公式：见正文]-极值点的完整描述。结果表明，一个单位EB映射[公式：见正文]是[公式：看正文]-极值当且仅当它的Choi秩等于[公式：见正文]。最后，作为EB映射的Holevo形式的直接结果，我们导出了单位EB映射集的[公式：见正文]-凸性的Krein–Milman定理的非交换类似物。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Reviews in Mathematical Physics 物理-物理：数学物理

CiteScore

3.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Reviews in Mathematical Physics fills the need for a review journal in the field, but also accepts original research papers of high quality. The review papers - introductory and survey papers - are of relevance not only to mathematical physicists, but also to mathematicians and theoretical physicists interested in interdisciplinary topics. Original research papers are not subject to page limitations provided they are of importance to this readership. It is desirable that such papers have an expository part understandable to a wider readership than experts. Papers with the character of a scientific letter are usually not suitable for RMP.