How machine learning can decipher complex quantum entanglement

Quantum entanglement, dubbed by Einstein as “spooky action at a distance”, is a resource driving the emerging field of quantum technologies. It is a peculiar form of correlations that can only exist in the quantum world. The weirdness is that entangled objects observed individually look completely random, yet display very strong correlations -- in fact, taken together they can literally be considered as multiple faces of the same object. Despite many applications in both quantum technologies and fundamental science, direct measurement of quantum entanglement is very challenging and is only partially solved for the case when the whole collection of atoms is in a certain quantum state. 

In a recent paper by Professor Abolfazl Bayat, from the Institute of Fundamental and Frontier sciences at the UESTC, and his collaborators at the University College London, published in Physical Review Letters [1], a novel approach for directly measuring entanglement for arbitrary quantum states has been put forward. The proposal has two steps: (i) performing a number of measurements, proportional to the system size, on a few copies of the system; and (ii) estimating the entanglement from the measurement results using machine learning, specifically neural networks. A schematic of the proposal is shown in the figure below. The nonlinear nature of the entanglement makes the use of neural networks very efficient in both equilibrium and non-equilibrium regimes. 


Fig. 1: In order to measure entanglement between subsystems A and B, quantified by logarithmic negativity, one has to measure two sets of measurements in opposite directions on each of the subsystems. The results of the measurements will be used by a pre-trained neural network to estimate logarithmic entanglement.  


[1] J. Gray, L. Banchi, A. Bayat, and S. Bose, Phys. Rev. Lett. 121, 150503 (2018).