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  • Open Access

Certifying Localizable Quantum Properties with Constant Sample Complexity

Zhenyu Du1, Jinchang Liu2, Elias X. Huber3, Zi-Wen Liu4,*, and Xiongfeng Ma1,†

  • *Contact author: zwliu0@tsinghua.edu.cn
  • †Contact author: xma@tsinghua.edu.cn
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Phys. Rev. X 16, 041027 – Published 27 October, 2026

DOI: https://doi.org/10.1103/rkl6-hfrn

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(n4) samples. Our unified framework provides both a practical toolkit for large-scale quantum certification and a novel lens into complex many-body systems.

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Popular Summary

Certifying crucial quantum resources produced by laboratory devices is a fundamental task. Yet, doing so for increasingly complex systems typically places high demands on experiments. How can we verify them with minimal experimental requirements? We develop a unified approach based on the principle of “localizable quantumness,” where measuring most qubits collapses the system’s state, concentrating signatures of its global properties into a few remaining qubits. These few qubits then serve as a compact fingerprint of the whole system, allowing us to efficiently certify essential features of the global state, such as entanglement and state fidelity. Remarkably, using simple single-qubit measurements, our method requires only a constant number of experimental repetitions, regardless of system size. Our framework thus establishes small subsystems as powerful probes into global quantum behavior, offering a practical path toward certifying large-scale quantum computers and simulators.

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Phys. Rev. X 16, 041027– Published 27 October, 2026
  • Received 1 October 2025
  • Revised 23 July 2026
  • Accepted 16 September 2026
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