A Separability-Entanglement Classifier via Machine Learning

Abstract: The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial transpose (PPT) criterion and the k-symmetric extendibility criterion to tackle this problem in practice, none of them enables a general, effective solution to the problem even for small dimensions. Explicitly, separable states form a high-dimensional convex set, which exhibits a vastly complicated structure. In this work, we build a new separability-entanglement classifier underpinned by machine learning techniques. Our method outperforms the existing methods in generic cases in terms of both speed and accuracy, opening up the avenues to explore quantum entanglement via the machine learning approach.