  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 of neural networks
are the outcome statistics data produced by locally measuring target quantum
states, and the training labels are well-chosen quantities. For bipartite
quantum states, this quantity is coherent information, which is a lower bound
for the entanglement of formation and 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 states, and can beat previous
approaches like semi-device-independent protocols for this problem easily in
both precision and application range. We also observe a surprising 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.
