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arXiv · 2610.05280

Quantum n-coloring is undecidable for every n $\ge$ 3

Christian Bo Kidmose-Frederiksen·Alfred Leth Nielsen
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Abstract

The quantum $n$-coloring problem, given graph $G$, asks whether there exists a perfect quantum strategy for the $n$-coloring game of $G$. Previously it was known that quantum $n$-coloring is undecidable only for $n=3$. We extend this to all $n\geq 3$ with one elementary reduction. Letting $G'=(G\square K_3)\lor K_{n-3}$, we show that $G$ is quantum $3$-colorable if and only if $G'$ is quantum $n$-colorable.

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Christian Bo Kidmose-Frederiksen, Alfred Leth Nielsen. 2026-10-04. Quantum n-coloring is undecidable for every n $\ge$ 3. https://arxiv.org/abs/2610.05280

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