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.
Related
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BibTeX
@misc{scala2026finitesize,
title = {{Finite-size Entanglement Certification via Third-Order Local Randomized Measurements}},
author = {Giovanni Scala and Corrado Cosimo Mattiacci and Dorota Pietryka and Gniewomir Sarbicki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08635},
eprint = {2609.08635},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08635},
}
RIS
TY - UNPB
TI - Finite-size Entanglement Certification via Third-Order Local Randomized Measurements
AU - Giovanni Scala
AU - Corrado Cosimo Mattiacci
AU - Dorota Pietryka
AU - Gniewomir Sarbicki
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.08635
UR - https://arxiv.org/abs/2609.08635
AB - 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.
ER -