Machine Learning Assisted Many-Body Entanglement Measurement

TL;DR

This paper introduces a machine learning method that efficiently measures entanglement in many-body quantum systems using significantly fewer measurements than traditional tomography, without prior state knowledge.

Contribution

It presents a neural network-based approach to estimate entanglement, specifically logarithmic negativity, with linear measurement complexity, applicable to diverse many-body systems.

Findings

Achieves entanglement measurement with O(N_A + N_B) measurements

Does not require prior knowledge of the quantum state

Applicable to both equilibrium and non-equilibrium systems

Abstract

Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of quantum correlations in many-body systems. However, in an experiment, the only way of measuring entanglement in a generic mixed state is through reconstructive quantum tomography, requiring an exponential number of measurements in the system size. Here, we propose a machine learning assisted scheme to measure the entanglement between arbitrary subsystems of size $N_A$ and $N_B$, with $\mathcal{O}(N_A + N_B)$ measurements, and without any prior knowledge of the state. The method exploits a neural network to learn the unknown, non-linear function relating certain measurable moments and the logarithmic negativity. Our procedure will allow entanglement measurements in a wide variety of systems, including strongly interacting many body systems in both equilibrium and non-equilibrium regimes.