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arXiv · 2609.08635

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

Giovanni Scala·Corrado Cosimo Mattiacci·Dorota Pietryka·Gniewomir Sarbicki
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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.

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Giovanni Scala, Corrado Cosimo Mattiacci, Dorota Pietryka, Gniewomir Sarbicki. 2026-09-08. Finite-size Entanglement Certification via Third-Order Local Randomized Measurements. https://arxiv.org/abs/2609.08635

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