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Entanglement is a key property in the development of quantum technologies andin the study of quantum many-body simulations. However, entanglementmeasurement typically requires quantum full-state tomography (FST). Here wepresent a neural network-assisted protocol for measuring entanglement inequilibrium and non-equilibrium states of local Hamiltonians. Instead of FST,it can learn comprehensive entanglement quantities from single-qubit ortwo-qubit Pauli measurements, such as R\'enyi entropy, partially-transposed(PT) moments, and coherence. It is also exciting that our neural network isable to learn the future entanglement dynamics using only single-qubit tracesfrom the previous time. In addition, we perform experiments using a nuclearspin quantum processor and train an adoptive neural network to studyentanglement in the ground and dynamical states of a one-dimensional spinchain. Quantum phase transitions (QPT) are revealed by measuring staticentanglement in ground states, and the entanglement dynamics beyond measurementtime is accurately estimated in dynamical states. These precise resultsvalidate our neural network. Our work will have a wide range of applications inquantum many-body systems, from quantum phase transitions to intriguingnon-equilibrium phenomena such as quantum thermalization.

Measuring Quantum Entanglement from Local Information by Machine Learning