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arXiv · 2510.23736

The injective norm of CSS quantum error-correcting codes

Stephane Dartois·Gilles Zémor
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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 computed exactly in condensed-matter theory - notably in the context of topological phases - for the Kitaev code and its extensions, in works by Or\'us 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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Stephane Dartois, Gilles Zémor. 2025-10-27. The injective norm of CSS quantum error-correcting codes. https://arxiv.org/abs/2510.23736

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