The injective norm of CSS quantum error-correcting codes
Stephane Dartois, Gilles Zémor
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Source: Crossref
Published: Sep 17, 2026
DOI: 10.1088/1751-8121/aea941
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Abstract In this paper, we compute the injective norm --a.k.a. geometric entanglement -- of standard basis states of CSS quantum error-correcting codes. The injective norm of a quantum state is a measure of genuine multipartite entanglement. Computing this measure is generically NP-hard. However, it has been exactly computed in condensed matter theory - notably in the context of topological phases -for the Kitaev code and its extensions, in works by Orús and collaborators. We extend these results to all CSS codes and thereby obtain the injective norm for a nontrivial, infinite family of quantum states. In doing so, we uncover an interesting connection to matroid theory and Edmonds' intersection theorem.
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