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

• URL: http://arxiv.org/abs/2609.08635v2
• Date: Fri, 11 Sep 2026 13:34:52 GMT
• Title: Finite-size Entanglement Certification via Third-Order Local Randomized Measurements
• Abstract summary: Certifying entanglement in high-dimensional systems usually requires full state tomography.<n>We derive a finite-size entanglement certificate that extends local randomized measurements to third order.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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