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

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.

Quantum Physics (quant-ph); Combinatorics (math.CO)

arXiv:2610.05280 [quant-ph]

(or arXiv:2610.05280v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.05280 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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