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Finite-size Entanglement Certification via Third-Order Local Randomized Measurements

Year: 2026

Type: preprint

Abstract: Certifying entanglement in high-dimensional systems usually requires full state tomography, whose cost grows rapidly with the system dimension. Local randomized measurements offer a scalable alternative, but existing tests based on second-order correlations access only limited information about the state. Here, we derive a finite-size entanglement certificate that extends local randomized measurements to third order. The additional third-order information reveals entanglement that remains undetected at second order, while a dimension-independent concentration bound provides rigorous control of finite-sample errors. Our result opens a practical route to extracting stronger entanglement information from experimental platforms without the dimension-dependent overhead of state tomography.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.08635

Authors: Scala, Giovanni, Mattiacci, Corrado Cosimo, Pietryka, Dorota, Sarbicki, Gniewomir

Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Bari, Polytechnic University of Bari, University of Bari Aldo Moro, University of Gdańsk, Nicolaus Copernicus University, Institute of Physics, Nicolaus Copernicus Astronomical Center

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Istituto Nazionale di Fisica Nucleare, HORIZON EUROPE Framework Programme

Awards: G6251103608, Quantum Secure Networks Partnership

OpenAlex ID: W7212009158

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