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

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.

arXiv:2609.08635 [quant-ph]

(or arXiv:2609.08635v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.08635 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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