Higher-rank numerical ranges and compression problems

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Abstract

We consider higher-rank versions of the standard numerical range for matrices. A central motivation for this investigation comes from quantum error correction. We develop the basic structure theory for the higher-rank numerical ranges, and give a complete description in the Hermitian case. We also consider associated projection compression problems.

AMS classification

15A60
15A90
47A12
81P68

Keywords

Hilbert space
Hermitian matrices
Normal matrices
Higher-rank numerical range
Compression-values
Dilations
Quantum error correction

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