# Detecting quantum entanglement with unsupervised learning

arXiv: https://arxiv.org/abs/2103.04804 · HTML: https://mlsanity.com/paper/2103.04804/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 46 references that are in the map.
- First posted on arXiv 8 Mar 2021.

## Builds on (most cited first, 7 of 7)

- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [A quantum-inspired classical algorithm for recommendation systems](https://mlsanity.com/paper/1807.04271/) (2018)
- [Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines](https://mlsanity.com/paper/1610.02746/) (2016)
- [Identifying Corresponding Patches in SAR and Optical Images with a Pseudo-Siamese CNN](https://mlsanity.com/paper/1801.08467/) (2018)
- [Transforming Bell's Inequalities into State Classifiers with Machine Learning](https://mlsanity.com/paper/1705.00813/) (2017)
- [Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement](https://mlsanity.com/paper/1901.09510/) (2019)

## Built on by (most cited first, 9 of 9)

- [Systematic Literature Review: Quantum Machine Learning and its applications](https://mlsanity.com/paper/2201.04093/) (2022)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Quantum neural network autoencoder and classifier applied to an industrial case study](https://mlsanity.com/paper/2205.04127/) (2022)
- [QuFeX: Quantum feature extraction module for hybrid quantum-classical deep neural networks](https://mlsanity.com/paper/2501.13165/) (2025)
- [Identification of quantum entanglement with Siamese convolutional neural networks and semi-supervised learning](https://mlsanity.com/paper/2210.07410/) (2022)
- [Data-driven criteria for quantum correlations](https://mlsanity.com/paper/2307.11091/) (2023)
- [Large-Scale Quantum Separability Through a Reproducible Machine Learning Lens](https://mlsanity.com/paper/2306.09444/) (2023)
- [On the Generalization Limits of Quantum Generative Adversarial Networks with Pure State Generators](https://mlsanity.com/paper/2508.09844/) (2025)
- [Entanglement Detection with Quantum-inspired Kernels and SVMs](https://mlsanity.com/paper/2508.17909/) (2025)

## Abstract (arXiv)

Quantum properties, such as entanglement and coherence, are indispensable resources in various quantum information processing tasks. However, there still lacks an efficient and scalable way to detecting these useful features, especially for high-dimensional and multipartite quantum systems. In this work, we exploit the convexity of samples without the desired quantum features and design an unsupervised machine learning method to detect the presence of such features as anomalies. Particularly, in the context of entanglement detection, we propose a complex-valued neural network composed of pseudo-siamese network and generative adversarial net, and then train it with only separable states to construct non-linear witnesses for entanglement. It is shown via numerical examples, ranging from two-qubit to ten-qubit systems, that our network is able to achieve high detection accuracy which is above 97.5% on average.Moreover, it is capable of revealing rich structures of entanglement, such as partial entanglement among subsystems. Our results are readily applicable to the detection of other quantum resources such as Bell nonlocality and steerability, and thus our work could provide a powerful tool to extract quantum features hidden in multipartite quantum data.