Certifying localizable quantum properties with constant sample complexity

Characterizing increasingly complex quantum systems is a central task in quantum information science, yet experimental costs often scale prohibitively with system size. Certifying key properties using simple local measurements is highly desirable but challenging. In this work, we introduce a highly general certification framework based on a physical phenomenon that we call localizable quantumness: for generic many-body states, essential quantum properties are robustly preserved within the projected ensembles on small subsystems after performing local projective measurements on the rest of the system. Leveraging this insight, we develop certification protocols that certify global properties -- including multipartite entanglement, circuit complexity, and quantum magic -- by witnessing them on a small, accessible subsystem. Our method dramatically reduces experimental cost by relying solely on local Pauli measurements, while achieving constant sample complexity, constant-level robustness, and soundness for mixed states -- exponentially improving the sample complexity and overcoming major limitations of previous methods. We further propose a random-basis variant for certifying state fidelity. We rigorously prove its constant sample complexity and robustness for random graph states via a novel error localization mechanism, with strong numerical evidence extending these results to generic states, which represent a substantial improvement over existing methods. Our results provide a practical, scalable toolkit for certifying large-scale quantum processors and offer a novel lens for understanding complex many-body quantum systems.