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This research introduces a framework for certifying global quantum properties like entanglement and circuit complexity using only local measurements on small subsystems. By leveraging the phenomenon of "localizable quantumness," it achieves constant sample complexity ($O(1)$), drastically reducing experimental costs compared to traditional $O(n^4)$ scaling methods required by state-of-the-art protocols for large systems.
Certifying localizable quantum properties with constant sample complexity
arXiv:2509.17580v3 Announce Type: replace Abstract: 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 protocols to certify global properties -- including multipartite entanglement, circuit complexity, and quantum magic -- by witnessing them on a small, accessible subsystem. Remarkably, randomizing the local measurement bases extends this capability to certify state fidelity. Relying solely on local Pauli measurements, these protocols achieve constant sample complexity and robustness for almost all quantum states, including a wide range of physically relevant states. For certifying the fidelity of $n$-qubit states, this $O(1)$ scaling dramatically improves upon state-of-the-art protocols requiring $O(n^4)$ samples. Our unified framework provides both a practical toolkit for large-scale quantum certification and a novel lens into complex many-body systems.
Abstract: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 protocols to certify global properties -- including multipartite entanglement, circuit complexity, and quantum magic -- by witnessing them on a small, accessible subsystem. Remarkably, randomizing the local measurement bases extends this capability to certify state fidelity. Relying solely on local Pauli measurements, these protocols achieve constant sample complexity and robustness for almost all quantum states, including a wide range of physically relevant states. For certifying the fidelity of $n$-qubit states, this $O(1)$ scaling dramatically improves upon state-of-the-art protocols requiring $O(n^4)$ samples. Our unified framework provides both a practical toolkit for large-scale quantum certification and a novel lens into complex many-body systems.
54 pages, 9 figures. V3: Solves Conjecture 1 from the previous version and proves that Haar-random states can be certified with constant sample complexity and robustness
arXiv:2509.17580 [quant-ph]
(or arXiv:2509.17580v3 [quant-ph] for this version)
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