Structural Lower Bounds for Quantum Property Estimation with Persistent Memory

arXiv:2611.05792v1 Announce Type: new Abstract: In quantum property estimation, an experimenter estimates $\operatorname{Tr}(O\rho)$ for a family of observables from independent copies of an unknown state $\rho$ simultaneously to additive error $\epsilon$. While quantum memory can dramatically reduce sample complexity, understanding the power of a modest register that remains coherent throughout an adaptive experiment has remained an open challenge because existing frameworks require optimizing over the infinite space of measurement trees. We overcome this barrier by developing a backward-induction framework based on operator resolvents.