In multipartite scenarios in entanglement theory, one has to consider separability with respect to different partitions, which results in a more complicated structure of the state space than in bipartite scenarios. There, states exhibiting genuine multipartite entanglement (GME) form a non-convex complement to a convex set of biseparable states (convex hull of all states that are separable with respect to some bipartition).
Superactivation of GME is a phenomenon whereby multiple shared copies of certain biseparable states can exhibit GME [1, 2].

In the original work, the main method to detect GME activation was to apply local projections from the multi-copy space to reduce the problem to detecting GME in the single-copy space. We systematically analyze the efficiency and limitations of this approach by comparing the detection in the multi-copy space with that of the projected single-copy space by different local projections [3]. Further, we introduce and answer the question of incompressible entanglement (ICE) - the existence of biseparable states that exhibit GME in k-copy space but that cannot be reduced to single-copy space by any projection. This result connects GME activation to entanglement distillation. In addition, we explore ”how much” GME can be generated through multi-copy activation by analyzing which SLOCC classes can be reached in this process.

Furthemore, we also extend the original work on GME multi-copy activation from finitedimensional Hilbert spaces to infinite-dimensional Hilbert spaces, namely for continuousvariable systems [4]. Beyond extension of the general proof, we provide examples of GME-activatable non-Gaussian states. For Gaussian states, we apply a necessary biseparability criterion for the covariance matrix [5] and show that it cannot detect GME activation. We further identify fully inseparable Gaussian states that satisfy the criterion but show that multiple and, in some cases, even single copies are GME. Thus, we show that the covariance-matrix biseparability criterion is not sufficient even for Gaussian states.

[1] Yamasaki, H.; Morelli, S.; Miethlinger, M.; Bavaresco, J.; Friis, N.; Huber, M. Quantum 2022, 6, 695.
[2] Palazuelos, C.; de Vicente, J. I. Quantum 2022, 6, 735.
[3] Weinbrenner, T. L.; Baksová, Klára; Denker, S.; Morelli, S.; Yu, X.-D.; Friis, N.; Guhne, O. ArXiv 2024, 2412.18331.
[4] Baksová, Klára; Leskovjanová, O.; Mišta Jr., L.; Agudelo, E.; Friis, N.  Quantum 2025, 9, 1699.
[5] Hyllus, P.; Eisert, J. New J. Phys. 2006, 8, 51.