Data-driven approach to mixed-state multipartite entanglement characterisation

TL;DR

This paper introduces a statistical manifold learning method to analyze and characterize the complex entanglement structures of mixed quantum states using measurable correlation data from quantum computers, revealing a sharp boundary between entangled and separable states.

Contribution

It presents a novel data-driven framework that leverages manifold learning to extract and quantify multipartite entanglement from experimental correlation data.

Findings

Correlation data suffices to characterize entanglement

Sharp boundary between entangled and separable states in embedding space

Multipartite entanglement is robust to finite noise

Abstract

We develop a statistical framework, based on a manifold learning embedding, to extract relevant features of multipartite entanglement structures of mixed quantum states from the measurable correlation data of a quantum computer. We show that the statistics of the measured correlators contains sufficient information to characterise the entanglement, and to quantify the mixedness of the state of the computer's register. The transition to the maximally mixed regime, in the embedding space, displays a sharp boundary between entangled and separable states. Away from this boundary, the multipartite entanglement structure is robust to finite noise.