Certification from strictly local probes

Ascertain whether there exists an efficient certification algorithm for k‑local n‑qubit Hamiltonians that, using only the dynamics observed through a strictly local probe (e.g., a single site or constant‑size subsystem) during evolution under H, can decide whether H equals a specified k‑local H0 or is ε‑far in normalized Frobenius norm, and characterize any quantitative tradeoff between probe size and certification complexity.

Background

Motivated by recent Hamiltonian learning results showing meaningful reconstruction from single‑site or constant‑size probes, the authors consider certification under similarly restricted access.

They pose whether certification remains efficient with strictly local probes and whether probe size impacts the achievable evolution‑time or sample complexity, aiming to bridge theory with experimentally realistic access constraints.