Experimentally accessible non-separability criteria for multipartite entanglement structure detection

TL;DR

This paper introduces an experimentally feasible, scalable method to detect multipartite entanglement structures in quantum states, validated through experiments on IBM quantum computers with various states.

Contribution

It presents a novel iterative approach and an algorithm for identifying non-separability and minimal partitions, applicable to current NISQ devices.

Findings

Successfully tested on 20-qubit IBM quantum computer

Revealed entanglement structures in 4-qubit and 8-qubit states

Demonstrated practical use of informationally complete POVMs on NISQ devices

Abstract

The description of the complex separability structure of quantum states in terms of partially ordered sets has been recently put forward. In this work, we address the question of how to efficiently determine these structures for unknown states. We propose an experimentally accessible and scalable iterative methodology that identifies, on solid statistical grounds, sufficient conditions for non-separability with respect to certain partitions. In addition, we propose an algorithm to determine the minimal partitions (those that do not admit further splitting) consistent with the experimental observations. We test our methodology experimentally on a 20-qubit IBM quantum computer by inferring the structure of the 4-qubit Smolin and an 8-qubit W states. In the first case, our results reveal that, while the fidelity of the state is low, it nevertheless exhibits the partitioning structure expected from the theory. In the case of the W state, we obtain very disparate results in different runs on the device, which range from non-separable states to very fragmented minimal partitions with little entanglement in the system. Furthermore, our work demonstrates the applicability of informationally complete POVM measurements for practical purposes on current NISQ devices.