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Quantum lower bounds for sinkless orientation in the quantum-LOCAL model

Establish nontrivial quantum lower bounds on the round complexity of finding sinkless orientations in the quantum-LOCAL model, using approaches beyond round elimination, which the paper shows cannot be used to derive such bounds.

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Background

By demonstrating that round elimination cannot serve as a proof technique in the quantum-LOCAL model, the authors identify a barrier to addressing several major open questions in distributed quantum advantage.

Among these, proving quantum lower bounds for sinkless orientations remains a prominent target that requires new methods beyond round elimination.

References

This also represents a new formal barrier for resolving major open questions related to distributed quantum advantage: it is not possible to prove quantum lower bounds for e.g. 3-coloring cycles or for finding sinkless orientations by constructing a round elimination sequence.

— Distributed Quantum Advantage for Local Problems (2411.03240 - Balliu et al., 5 Nov 2024) in Implications and discussion, Lower-bound proof techniques paragraph