A class of Schwarz qubit maps with diagonal unitary and orthogonal symmetries

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-09-09 DOI:10.1088/1751-8121/ad75d6
Dariusz Chruściński and Bihalan Bhattacharya
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Abstract

A class of unital qubit maps displaying diagonal unitary and orthogonal symmetries is analyzed. Such maps have already found a lot applications in quantum information theory. We provide a complete characterization of this class of maps showing intricate relation between positivity, operator Schwarz inequality, and complete positivity. Finally, it is shown how to generalize the entire picture beyond unital case (so called generalized Schwarz maps). Interestingly, the first example of Schwarz but not completely positive map found by Choi belongs to our class. As a case study we provide a full characterization of Pauli maps. Our analysis leads to generalization of seminal Fujiwara–Algoet conditions for Pauli quantum channels.
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一类具有对角单元对称性和正交对称性的施瓦兹量子比特映射
本文分析了一类显示对角单元对称性和正交对称性的单元量子比特映射。这类映射已在量子信息论中得到广泛应用。我们提供了这一类映射的完整表征,显示了实在性、算子施瓦茨不等式和完全实在性之间错综复杂的关系。最后,我们还展示了如何将整个图景概括到单值情况之外(即所谓的广义施瓦茨映射)。有趣的是,Choi 发现的第一个施瓦茨但非完全正映射的例子就属于我们这一类。作为案例研究,我们对保利映射进行了全面描述。我们的分析导致了开创性的富士原-阿尔戈特条件对保利量子通道的广义化。
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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