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Open AccessArticle

On a Matrix Inequality Related to the Distillability Problem

by Yi Shen 1,† and Lin Chen 1,2,*,†
1
School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
2
International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2018, 20(8), 588; https://doi.org/10.3390/e20080588
Received: 25 May 2018 / Revised: 19 July 2018 / Accepted: 4 August 2018 / Published: 8 August 2018
(This article belongs to the Collection Quantum Information)
We investigate the distillability problem in quantum information in d 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 . View Full-Text
Keywords: matrix inequality; singular value; eigenvalue; Kronecker product; quantum information; distillability problem matrix inequality; singular value; eigenvalue; Kronecker product; quantum information; distillability problem
MDPI and ACS Style

Shen, Y.; Chen, L. On a Matrix Inequality Related to the Distillability Problem. Entropy 2018, 20, 588.

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