# Large-Scale Quantum Separability Through a Reproducible Machine Learning Lens

arXiv: https://arxiv.org/abs/2306.09444 · HTML: https://mlsanity.com/paper/2306.09444/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 35 references that are in the map.
- First posted on arXiv 15 Jun 2023.

## Builds on (most cited first, 2 of 2)

- [Detecting quantum entanglement with unsupervised learning](https://mlsanity.com/paper/2103.04804/) (2021)
- [Building separable approximations for quantum states via neural networks](https://mlsanity.com/paper/2112.08055/) (2021)

## Built on by (most cited first, 1 of 1)

- [Entanglement Detection with Quantum-inspired Kernels and SVMs](https://mlsanity.com/paper/2508.17909/) (2025)

## Abstract (arXiv)

The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in large-scale scenarios. We provide an efficient Frank-Wolfe-based algorithm to approximately seek the nearest separable density matrix and derive a systematic way for labeling density matrices as separable or entangled, allowing us to treat quantum separability as a classification problem. Our method is applicable to any two-qudit mixed states. Numerical experiments with quantum states of 3- and 7-dimensional qudits validate the efficiency of the proposed procedure, and demonstrate that it scales up to thousands of density matrices with a high quantum entanglement detection accuracy. This takes a step towards benchmarking quantum separability to support the development of more powerful entanglement detection techniques.