On a matrix inequality related to the distillability problem

Yi Shen; Lin Chen

doi:10.3390/e20080588

On a matrix inequality related to the distillability problem

Yi Shen
, Lin Chen^*

^*此作品的通讯作者

数学科学学院

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

5 引用（Scopus）

摘要

We investigate the distillability problem in quantum information in C^d ⊗ C^d. One case of the problem has been reduced to proving a matrix inequality when d = 4. We investigate the inequality for three families of non-normal matrices. We prove the inequality for the first two families with d = 4 and for the third family with d ≥ 5. We also present a sufficient condition for the fulfillment of the inequality with d = 4.

源语言	英语
文章编号	588
期刊	Entropy
卷	20
期	8
DOI	https://doi.org/10.3390/e20080588
出版状态	已出版 - 1 8月 2018

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abstract = "We investigate the distillability problem in quantum information in Cd ⊗ Cd. One case of the problem has been reduced to proving a matrix inequality when d = 4. We investigate the inequality for three families of non-normal matrices. We prove the inequality for the first two families with d = 4 and for the third family with d ≥ 5. We also present a sufficient condition for the fulfillment of the inequality with d = 4.",

keywords = "Eigenvalue, Kronecker product, Matrix inequality, Quantum information; distillability problem, Singular value",

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AB - We investigate the distillability problem in quantum information in Cd ⊗ Cd. One case of the problem has been reduced to proving a matrix inequality when d = 4. We investigate the inequality for three families of non-normal matrices. We prove the inequality for the first two families with d = 4 and for the third family with d ≥ 5. We also present a sufficient condition for the fulfillment of the inequality with d = 4.

KW - Eigenvalue

KW - Kronecker product

KW - Matrix inequality

KW - Quantum information; distillability problem

KW - Singular value

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On a matrix inequality related to the distillability problem

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