Experimental determination of multipartite entanglement with incomplete information

TL;DR

This paper experimentally investigates how much multipartite entanglement information can be obtained with incomplete measurements, demonstrating practical utility even under non-ideal conditions.

Contribution

It experimentally tests a method to detect multipartite entanglement without full correlation measurements using an optical setup.

Findings

Incomplete measurements can effectively witness multipartite entanglement.

The method works for non-pure states and under measurement imperfections.

Complete state tomography is compared with incomplete approaches.

Abstract

Multipartite entanglement is very poorly understood despite all the theoretical and experimental advances of the last decades. Preparation, manipulation and identification of this resource is crucial for both practical and fundamental reasons. However, the difficulty in the practical manipulation and the complexity of the data generated by measurements on these systems increase rapidly with the number of parties. Therefore, we would like to experimentally address the problem of how much information about multipartite entanglement we can access with incomplete measurements. In particular, it was shown that some types of pure multipartite entangled states can be witnessed without measuring the correlations [M. Walter et al., Science 340, 1205 (2013)] between parties, which is strongly demanding experimentally. We explore this method using an optical setup that permits the preparation and the complete tomographic reconstruction of many inequivalent classes of three- and four-partite entangled states, and compare complete versus incomplete information. We show that the method is useful in practice, even for non-pure states or non ideal measurement conditions.