Correlation-pattern-based Continuous-variable Entanglement Detection through Neural Networks

TL;DR

This paper introduces a neural network-based method for detecting entanglement in continuous-variable quantum states, including non-Gaussian states, using correlation patterns, which outperforms traditional techniques in accuracy and efficiency.

Contribution

The authors develop a neural network approach that effectively detects entanglement in both Gaussian and non-Gaussian states using correlation patterns, avoiding full state tomography.

Findings

Higher accuracy than maximum-likelihood tomography in entanglement detection

Effective on a wide class of Gaussian and non-Gaussian states

Clear boundary between entangled and non-entangled states after neural network processing

Abstract

Entanglement in continuous-variable non-Gaussian states provides irreplaceable advantages in many quantum information tasks. However, the sheer amount of information in such states grows exponentially and makes a full characterization impossible. Here, we develop a neural network that allows us to use correlation patterns to effectively detect continuous-variable entanglement through homodyne detection. Using a recently defined stellar hierarchy to rank the states used for training, our algorithm works not only on any kind of Gaussian state but also on a whole class of experimentally achievable non-Gaussian states, including photon-subtracted states. With the same limited amount of data, our method provides higher accuracy than usual methods to detect entanglement based on maximum-likelihood tomography. Moreover, in order to visualize the effect of the neural network, we employ a dimension reduction algorithm on the patterns. This shows that a clear boundary appears between the entangled states and others after the neural network processing. In addition, these techniques allow us to compare different entanglement witnesses and understand their working. Our findings provide a new approach for experimental detection of continuous-variable quantum correlations without resorting to a full tomography of the state and confirm the exciting potential of neural networks in quantum information processing.