Generic lower bound technique for quantum-LOCAL and stronger locality models

Develop a generic lower bound technique for locally checkable problems in the quantum-LOCAL model and in models stronger than quantum-LOCAL, providing a broadly applicable method to prove post-quantum lower bounds across the locality landscape.

Background

The paper surveys the landscape of locality models (including LOCAL, quantum-LOCAL, non-signaling, bounded-dependence, SLOCAL, dynamic-LOCAL, and online-LOCAL) and notes that current lower bound tools for quantum-LOCAL are limited to specialized arguments (e.g., indistinguishability and existential graph theory) and do not yield a widely applicable framework for core problems like coloring or the Lovász Local Lemma.

In contrast to the LOCAL model—where round elimination serves as a generic technique—recent work shows that round elimination cannot be used to prove quantum-LOCAL lower bounds. The authors therefore articulate the need for a genuinely new, broadly applicable lower bound technique for quantum-LOCAL (ideally already applicable in the strongest model, randomized online-LOCAL).