Stéphane Dartois: On the injective norm of CSS code states

mercredi 4 févr. 2026, 14:00 → 15:00 Europe/Paris

The injective norm, also known as geometric entanglement, is a measure of genuinely multipartite entanglement of a quantum state. It can be seen as a natural generalization of the infinite order Rényi entropy (equivalently, the largest Schmidt coefficient) beyond the bipartite setting. This quantity appears in several areas, for instance:

1. as a probe for phase transitions in topologically ordered materials;

2. in quantum complexity theory, where it encodes how well a QMA witness can be approximated by a structured (and NP-hard to optimize over) class of states;

3. and in quantum algorithms, where it drives the probability of success of Grover’s algorithm when the input state is fixed.

However, the computation of this measure of entanglement is generically a NP-hard problem and its properties are not well understood. In this talk, I will show that the injective norm can be computed efficiently for any computational basis state in the CSS code subspace. In the process, I will describe a surprising connection to matroid theory. If time allows, I will also review related results of the literature.