Graph Quantum Magic Squares and Free Spectrahedra
Mathematical Physics
2026-03-04 v3 math.MP
Operator Algebras
Abstract
Recently De les Coves, Drescher and Netzer showed that an analogue of the Birkhoff--von Neumann theorem fails in the quantum setting. Motivated by this and questions arising in the study of quantum automorphisms of graphs, we introduce a graph-based variant of quantum magic squares and show that the analogue already fails for the cycle , via an explicit counterexample. We also show that they admit monic linear matrix inequality descriptions, hence form compact free spectrahedra.
Cite
@article{arxiv.2512.08797,
title = {Graph Quantum Magic Squares and Free Spectrahedra},
author = {Francesca La Piana},
journal= {arXiv preprint arXiv:2512.08797},
year = {2026}
}
Comments
24 pages. Minor corrections, typos, and minor revisions to the exposition