On a matrix inequality related to the distillability problem

Yi Shen; Lin Chen

doi:10.3390/e20080588

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arXiv · 1708.03863

On a matrix inequality related to the distillability problem

Yi Shen·Lin Chen

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Abstract

We investigate the distillability problem in quantum information in $\bbC^d\ox\bbC^d$. A special case of the problem has been reduced to proving a matrix inequality when $d=4$. We investigate the inequality for two families of non-normal matrices. We prove the inequality for the first family with $d=4$ and two special cases of the second family with $d\ge4$. We also prove the inequality for all normal matrices with $d>4$.

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Yi Shen, Lin Chen. 2017-08-13. On a matrix inequality related to the distillability problem. https://doi.org/10.3390/e20080588

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