Superlogarithmic Gap Result for LCLs on Trees in Quantum-LOCAL

Francesco d'Amore; Henrik Lievonen

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arXiv · 2608.16854

Superlogarithmic Gap Result for LCLs on Trees in Quantum-LOCAL

Francesco d'Amore·Henrik Lievonen

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Abstract

We show that, on trees, any locally checkable labeling problem (LCL) $\Pi$ that can be solved by an $n^{o(1)}$-dependent distribution can also be solved by an $O(\log n)$-round deterministic LOCAL algorithm. The result is obtained through a rake-and-compress-style decomposition of the input tree, and local simulations of the bounded dependent distribution on the components of the decomposition. As a corollary to our result, any LCL problem on trees can either be solved by an $O(\log n)$ deterministic LOCAL algorithm, or requires $n^{\Omega(1)}$ rounds to solve by a quantum-LOCAL algorithm.

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BibTeX RIS

Francesco d'Amore, Henrik Lievonen. 2026-08-17. Superlogarithmic Gap Result for LCLs on Trees in Quantum-LOCAL. https://arxiv.org/abs/2608.16854

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