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

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 N there exist GME-activatable multipartite states of fixed (i.e. independent of k) local dimensions such that k copies of them remain biseparable.This research was funded by the Spanish Ministerio de Ciencia e Innovación (grant PID2020-113523GB-I00) and Comunidad de Madrid (grant QUITEMAD-CMS2018/TCS-4342). C.P. is partially supported as well by the Spanish Ministerio de Ciencia e Innovación (grant CEX2019-000904-S funded by MCINN/AEI/10.13039/501100011033). JIdV also acknowledges financial support from Comunidad de Madrid (Multiannual Agreement with UC3M in the line of Excellence of University Professors EPUC3M23 in the context of the V PRICIT)