Normal matrix compressions

TL;DR

This paper explores the theory of normal matrix compressions, extending the understanding from scalar to normal compressions, with detailed analysis of rank-two cases, rooted in quantum information theory.

Contribution

It introduces initial principles for normal matrix compressions and provides a detailed study specifically on rank-two normal compressions.

Findings

Established general principles for normal matrix compressions

Analyzed rank-two normal compressions in detail

Connected theory to quantum information error correction

Abstract

The recently developed theory of higher--rank numerical ranges originated in problems of error correction in quantum information theory but its mathematical implications now include a quite satisfactory understanding of \emph{scalar} compressions of complex matrices. Here our aim is to make some first steps in the more general program of understanding \emph{normal} compressions. We establish some general principles for the program and make a detailed study of rank--two normal compressions.