Activation of genuine multipartite entanglement: Beyond the single-copy paradigm of entanglement characterisation

TL;DR

This paper explores how access to multiple copies of a quantum state can activate genuine multipartite entanglement, revealing new properties and hierarchies beyond the single-copy paradigm in quantum entanglement characterization.

Contribution

It introduces the concept that multiple copies can activate genuine multipartite entanglement from partially separable states, extending the understanding beyond the traditional single-copy framework.

Findings

Multiple copies can activate entanglement from partially separable states.

More than two copies may be necessary to observe activation effects.

A hierarchy of activatable states is proposed, with an asymptotic collapse conjecture.

Abstract

Entanglement shared among multiple parties presents complex challenges for the characterisation of different types of entanglement. One of the most fundamental insights is the fact that some mixed states can feature entanglement across every possible cut of a multipartite system yet can be produced via a mixture of states separable with respect to different partitions. To distinguish states that genuinely cannot be produced from mixing such partition-separable states, the term genuine multipartite entanglement was coined. All these considerations originate in a paradigm where only a single copy of the state is distributed and locally acted upon. In contrast, advances in quantum technologies prompt the question of how this picture changes when multiple copies of the same state become locally accessible. Here we show that multiple copies unlock genuine multipartite entanglement from partially separable states, i.e., mixtures of the partition-separable states, even from undistillable ensembles, and even more than two copies can be required to observe this effect. With these findings, we characterise the notion of genuine multipartite entanglement in the paradigm of multiple copies and conjecture a strict hierarchy of activatable states and an asymptotic collapse of the hierarchy.