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arXiv:2512.08797

Graph Quantum Magic Squares and Free Spectrahedra

La Piana, Francesca

Published Dec 9, 2025• 0 citations
arXivHTMLPDF

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 \(C_4\), via an explicit counterexample. We also show that they admit monic linear matrix inequality descriptions, hence form compact free spectrahedra.

DOI
10.48550/arxiv.2512.08797

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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 (C_4), via an explicit counterexample. We also show that they admit monic linear matrix inequality descriptions, hence form compact free spectrahedra.
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