An Online Approach for Entanglement Verification Using Classical Shadows

Quantum Physics [Submitted on 27 Mar 2026] An Online Approach for Entanglement Verification Using Classical Shadows Marwa Marso, Sabrina Herbst, Jadwiga Wilkens, Vincenzo De Maio, Ivona Brandic, Richard Kueng Quantum measurements are slow, while classical processors are fast, yet existing hybrid protocols never exploit this asymmetry. In this work, we propose an alternative formulation of classical estimators as online algorithms that are updated incrementally upon obtaining a new sample. Classical shadows are the natural fit for this approach: designed around the principle of measuring first and asking questions later, each snapshot is a self-contained classical description that can be processed immediately and independently. As a first demonstration, we focus on mixed state entanglement verification via PT-moments, moments of the partially transposed density matrix that provide experimentally accessible sufficient conditions for entanglement. We construct two unbiased online estimators that together characterize the fundamental challenge between memory footprint and per-shot computational cost: one scales to large systems at low moment order, the other handles high moment orders at the expense of memory exponential in system size. The online estimator certifies entanglement reliably and, by exploiting all \binom{T}{m} combinations of snapshots, requires fewer samples than state-of-the-art baselines, turning entanglement detection from a purely offline diagnostic into a protocol that runs concurrently with the experiment. Comments: 20 pages, 10 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.26602 [quant-ph]   (or arXiv:2603.26602v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.26602 Focus to learn more Submission history From: Sabrina Herbst [view email] [v1] Fri, 27 Mar 2026 16:59:14 UTC (5,218 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)