Quantifying unknown entanglement by neural networks

Quantum entanglement plays a crucial role in quantum information processing tasks and quantum mechanics; hence, quantifying unknown entanglement is a fundamental task. However, this is also challenging, as entanglement cannot be measured by any observables directly. In this paper, we train neural networks to quantify unknown entanglement, where the input features for neural networks are the outcome statistics data produced by measuring target quantum states with local or even single-qubit Pauli observables, and the training labels are well-chosen quantities. For bipartite quantum states, this quantity is coherent information, which is a lower bound for many popular entanglement measures, like the entanglement of distillation. For multipartite quantum states, we choose this quantity as the geometric measure of entanglement. It turns out that the neural networks we train have very good performance in quantifying unknown quantum entanglement and can beat previous approaches like semi-device-independent protocols for this problem easily in both precision and application range. We also observe an interesting phenomenon that on quantum states with stronger quantum nonlocality, the neural networks tend to have better performance, though we do not provide them any knowledge on quantum nonlocality.