Operational Characterizations and Resource Structure of the Interactive Weight of Quantum Instruments

arXiv:2611.07371v1 Announce Type: new Abstract: Quantifying the interactivity of quantum instruments is fundamental to understanding their resource structure and operational capabilities. Here, we introduce the interactive weight of quantum instruments as a resource quantifier that measures the minimum fraction of an instrument that cannot be explained by non-interactive components. Through quantum-information tasks including quantum-state recovery, positive linear loss games, and environment-assisted input-blind extraction, we establish quantitative bounds on the interactive weight of quantum instruments and exact operational characterizations of its complementary quantity, the maximal non-interactive content.