English

Inequality for p-norms of positive matrices

Quantum Physics 2007-05-23 v2

Abstract

This paper derives an inequality relating the p-norm of a positive 2 x 2 block matrix to the p-norm of the 2 x 2 matrix obtained by replacing each block by its p-norm. The inequality had been known for integer values of p, so the main contribution here is the extension to all values p >= 1. In a special case the result reproduces Hanner's inequality. As an application in quantum information theory, the inequality is used to obtain some results concerning maximal p-norms of product channels.

Keywords

Cite

@article{arxiv.quant-ph/0302069,
  title  = {Inequality for p-norms of positive matrices},
  author = {C. King},
  journal= {arXiv preprint arXiv:quant-ph/0302069},
  year   = {2007}
}