Additivity violation of quantum channels via strong convergence to semi-circular and circular elements

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2021-01-02 DOI:10.1142/s2010326322500125

M. Fukuda, Takahiro Hasebe, Shinya Sato

引用次数: 1

Abstract

Additivity violation of minimum output entropy, which shows non-classical properties in quantum communication, had been proved in most cases for random quantum channels defined by Haar-distributed unitary matrices. In this paper, we investigate random completely positive maps made of Gaussian Unitary Ensembles and Ginibre Ensembles regarding this matter. Using semi-circular systems and circular systems of free probability, we not only show the multiplicativity violation of maximum output norms in the asymptotic regimes but also prove the additivity violation via Haagerup inequality for a new class of random quantum channels constructed by rectifying the above completely positive maps based on strong convergence.

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半圆和圆元强收敛量子通道的可加性破坏

对于由haar分布酉矩阵定义的随机量子信道，在大多数情况下证明了最小输出熵的可加性违反，它在量子通信中表现出非经典性质。在这篇文章中，我们研究了由高斯酉系综和吉尼布尔系综组成的随机完全正映射。利用半圆系统和自由概率的圆系统，我们不仅证明了在渐近区域最大输出模的乘性违反，而且通过Haagerup不等式证明了一类基于强收敛的完全正映射的随机量子通道的可加性违反。

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

Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.90

自引率

11.10%

发文量

期刊介绍： Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.