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arXiv · 2512.02977

On the ellipticity of the higher rank numerical range

Natália Bebiano·Rute Lemos·Graça Soares
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Abstract

The higher rank numerical range is a concept that generalizes the classical numerical range, and it has application in quantum error correction. We investigate these sets for $2$-by-$2$ block matrices with associated Kippenhahn curves consisting of ellipses (and eventually points). As a consequence, elliptical higher rank numerical range results are derived in a unified way, using an approach developed by Spitkovsky {\it et al}.

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Natália Bebiano, Rute Lemos, Graça Soares. 2025-12-02. On the ellipticity of the higher rank numerical range. https://doi.org/10.1016/j.jmaa.2026.130614

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