Related papers: The injective norm of CSS quantum error-correcting codes

The injective norm of CSS quantum error-correcting codes

URL: http://arxiv.org/abs/2510.23736v1
Date: Mon, 27 Oct 2025 18:06:02 GMT
Title: The injective norm of CSS quantum error-correcting codes
Authors: Stephane Dartois, Gilles Zémor,
Abstract summary: We compute the injective norm of standard basis states of CSS quantum error-correcting codes.<n>We extend these results to all CSS codes and thereby obtain the injective norm for a nontrivial, infinite family of quantum states.
Score: 8.450904497835262
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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