An Online Approach for Entanglement Verification Using Classical Shadows
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912985287491584 |
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| author | Marso, Marwa Herbst, Sabrina Wilkens, Jadwiga De Maio, Vincenzo Brandic, Ivona Kueng, Richard |
| author_facet | Marso, Marwa Herbst, Sabrina Wilkens, Jadwiga De Maio, Vincenzo Brandic, Ivona Kueng, Richard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26602 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Online Approach for Entanglement Verification Using Classical Shadows Marso, Marwa Herbst, Sabrina Wilkens, Jadwiga De Maio, Vincenzo Brandic, Ivona Kueng, Richard Quantum Physics 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. |
| title | An Online Approach for Entanglement Verification Using Classical Shadows |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.26602 |