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^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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.

Original language	English
Article number	588
Journal	Entropy
Volume	20
Issue number	8
DOIs	https://doi.org/10.3390/e20080588
State	Published - 1 Aug 2018

Keywords

Eigenvalue
Kronecker product
Matrix inequality
Quantum information; distillability problem
Singular value

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10.3390/e20080588

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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.",

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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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Keywords

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