Importance sampling of randomized measurements for probing entanglement

TL;DR

This paper introduces an improved method combining importance sampling with randomized measurements to efficiently characterize entanglement in larger quantum systems, significantly reducing measurement requirements and errors.

Contribution

It presents a novel approach that enhances entanglement measurement efficiency using importance sampling and classical techniques, enabling larger system analysis.

Findings

Doubles the effective subsystem sizes for entanglement measurement.

Reduces measurement count exponentially for purity estimation.

Achieves significant error reduction with classical machine learning and tensor networks.

Abstract

We show that combining randomized measurement protocols with importance sampling allows for characterizing entanglement in significantly larger quantum systems and in a more efficient way than in previous work. A drastic reduction of statistical errors is obtained using classical techniques of machine-learning and tensor networks using partial information on the quantum state. In present experimental settings of engineered many-body quantum systems this effectively doubles the (sub-)system sizes for which entanglement can be measured. In particular, we show an exponential reduction of the required number of measurements to estimate the purity of product states and GHZ states.