Improving shadow estimation with locally-optimal dual frames

Accurate estimation of observables in quantum systems is a central challenge in quantum information science, yet practical implementations are fundamentally constrained by the limited number of measurement shots. In this work we explore a variation of the classical shadows protocol in which the measurements are kept local while allowing the resulting classical shadows themselves to be correlated. By constructing locally optimal shadows, we obtain unbiased estimators that outperform state-of-the-art methods, achieving the same accuracy with substantially fewer measurements. We validate our approach through numerical experiments on molecular Hamiltonians with up to 40 qubits and a 50-qubit Ising model consistently observing significant reductions in estimation errors.