Genuine multipartite entanglement of quantum states in the multiple-copy scenario

TL;DR

This paper investigates the activation of genuine multipartite entanglement (GME) in the multiple-copy regime, revealing that GME activation depends on partial separability and can occur with a fixed number of copies regardless of the number of parties.

Contribution

It provides a simple characterization of GME-activatable states and demonstrates that no finite number of copies universally bounds GME activation in multipartite states.

Findings

GME-activatable states are exactly those not partially separable across some bipartition.

No finite upper bound exists on the number of copies needed for GME activation.

Existence of states that remain biseparable even after multiple copies, regardless of the number of parties.

Abstract

Genuine multipartite entanglement (GME) is considered a powerful form of entanglement since it corresponds to those states that are not biseparable, i.e.\ a mixture of partially separable states across different bipartitions of the parties. In this work we study this phenomenon in the multiple-copy regime, where many perfect copies of a given state can be produced and controlled. In this scenario the above definition leads to subtle intricacies as biseparable states can be GME-activatable, i.e.\ several copies of a biseparable state can display GME. We show that the set of GME-activatable states admits a simple characterization: a state is GME-activatable if and only if it is not partially separable across one bipartition of the parties. This leads to the second question of whether there is a general upper bound in the number of copies that needs to be considered in order to observe the activation of GME, which we answer in the negative. In particular, by providing an explicit construction, we prove that for any number of parties and any number $k\in\mathbb{N}$ there exist GME-activatable multipartite states of fixed (i.e.\ independent of $k$) local dimensions such that $k$ copies of them remain biseparable.