# Learning entanglement breakdown as a phase transition by confusion

arXiv: https://arxiv.org/abs/2202.00348 · HTML: https://mlsanity.com/paper/2202.00348/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 67 references that are in the map.
- First posted on arXiv 1 Feb 2022.

## Builds on (most cited first, 11 of 11)

- [Discovering Phase Transitions with Unsupervised Learning](https://mlsanity.com/paper/1606.00318/) (2016)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Machine learning & artificial intelligence in the quantum domain](https://mlsanity.com/paper/1709.02779/) (2017)
- [Mutual Information, Neural Networks and the Renormalization Group](https://mlsanity.com/paper/1704.06279/) (2017)
- [Neural-Network Quantum States, String-Bond States, and Chiral Topological States](https://mlsanity.com/paper/1710.04045/) (2017)
- [Transforming Bell's Inequalities into State Classifiers with Machine Learning](https://mlsanity.com/paper/1705.00813/) (2017)
- [Experimental quantum homodyne tomography via machine learning](https://mlsanity.com/paper/1907.06589/) (2019)
- [Probing hidden spin order with interpretable machine learning](https://mlsanity.com/paper/1804.08557/) (2018)
- [Speeding-up the decision making of a learning agent using an ion trap quantum processor](https://mlsanity.com/paper/1709.01366/) (2017)
- [Revealing quantum chaos with machine learning](https://mlsanity.com/paper/1902.09216/) (2019)
- [Learning Algebraic Models of Quantum Entanglement](https://mlsanity.com/paper/1908.10247/) (2019)

## Built on by (most cited first, 2 of 2)

- [Explainable Representation Learning of Small Quantum States](https://mlsanity.com/paper/2306.05694/) (2023)
- [Phase Transitions in the Output Distribution of Large Language Models](https://mlsanity.com/paper/2405.17088/) (2024)

## Abstract (arXiv)

Quantum technologies require methods for preparing and manipulating entangled multiparticle states. However, the problem of determining whether a given quantum state is entangled or separable is known to be an NP-hard problem in general, and even the task of detecting entanglement breakdown for a given class of quantum states is difficult. In this work, we develop an approach for revealing entanglement breakdown using a machine learning technique, which is known as 'learning by confusion'. We consider a family of quantum states, which is parameterized such that there is a single critical value dividing states within this family into separate and entangled. We demonstrate the 'learning by confusion' scheme allows us to determine the critical value. Specifically, we study the performance of the method for the two-qubit, two-qutrit, and two-ququart entangled state. In addition, we investigate the properties of the local depolarization and the generalized amplitude damping channel in the framework of the confusion scheme. Within our approach and setting the parameterization of special trajectories, we obtain an entanglement-breakdown 'phase diagram' of a quantum channel, which indicates regions of entangled (separable) states and the entanglement-breakdown region. Then we extend the way of using the 'learning by confusion' scheme for recognizing whether an arbitrary given state is entangled or separable. We show that the developed method provides correct answers for a variety of states, including entangled states with positive partial transpose. We also present a more practical version of the method, which is suitable for studying entanglement breakdown in noisy intermediate-scale quantum devices. We demonstrate its performance using an available cloud-based IBM quantum processor.