Machine learning detection of Gaussian steering in continuous-variable systems under data imbalance.

Gaussian steering in continuousvariable (CV) systems, as a quantum correlation between nonlocality and entanglement, is an important quantum resource. Rapid detection of Gaussian steering is a significant challenge in quantum information process. In this paper, we employ a combination of machine learning methods, including Support Vector Machine (SVM), Backpropagation Neural Network (BPNN) and Meta-Weight-Net Neural Network (MWN) to speed up the detection. An ensemble learning approach that integrates these methods is also utilized to increase the accuracy of detection. A computable Gaussian steering quantification [Formula: see text] introduced recently in [Phys. Rev. A 110, 052427] serves as a pivotal tool for labeling the samples. A key observation is that steerable Gaussian states are vastly outnumbered by unsteerable ones, particularly in configurations where the untrusted party possesses significantly more modes than the trusted party. This leads to a highly skewed distribution of sample states in the dataset. In response to this phenomenon and to make comparison, we propose the imbalance factor ξ and prepare three types of datasets to be trained: balanced datasets, naturally generated datasets and augmented datasets with [Formula: see text] via a data augmentation strategy. Numerical experiments for seven low modes scenarios reveal that the classifiers obtained by utilizing the ensemble learning method training on augmented dataset have the best overall performance, significantly improving generalization capabilities with low cost and high test accuracy, achieving detection times as fast as [Formula: see text] seconds, at least 100 times faster than calculating [Formula: see text]. The speed advantage of machine learning detection will be more obvious in the case of higher modes. Thus the approach is both efficient and reliable, offering valuable insights into the broader potential of machine learning applications in quantum information science and providing a robust framework for machine learning utilized to classification tasks, especially in data-imbalanced scenarios.