Multi-copy activation of genuine multipartite entanglement in continuous-variable systems

Klára Baksová; Olga Leskovjanová; Ladislav Mišta Jr.; Elizabeth Agudelo; Nicolai Friis

doi:10.22331/q-2025-04-09-1699

Multi-copy activation of genuine multipartite entanglement in continuous-variable systems

Klára Baksová¹, Olga Leskovjanová², Ladislav Mišta Jr.², Elizabeth Agudelo¹, and Nicolai Friis¹

¹Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Vienna, Austria
²Department of Optics, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic

Published:	2025-04-09, volume 9, page 1699
Editor:	Daniel McNulty
Eprint:	arXiv:2312.16570v5
Doi:	https://doi.org/10.22331/q-2025-04-09-1699
Citation:	Quantum 9, 1699 (2025).

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Updated after initial publication: This publication was updated to version v5 after the initial publication. The authors left the following comment on the arXiv:

8+11 pages, 2 figures; extended results, version accepted for publication

Abstract

Multi-copy activation of genuine multipartite entanglement (GME) is a phenomenon whereby multiple copies of biseparable but fully inseparable states can exhibit GME. This was shown to be generically possible in finite dimensions. Here, we extend this analysis to infinite dimensions. We provide examples of GME-activatable non-Gaussian states. For Gaussian states, we apply a necessary biseparability criterion for the covariance matrix 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.

Popular summary

Quantum entanglement is a type of correlation between two or more quantum systems that is of central importance for many quantum technologies. For two systems, all quantum states fall in one of two categories: they are either entangled or not entangled—separable. When more than two systems are involved—a situation that is both of practical and fundamental interest, the classification of quantum states is more complicated. Some states are separable for some partitions—groupings of quantum systems into two (or more) subsets—but not for another. For example, for three systems, A, B, and C, the pair (A,B) might be entangled with subsystem C, while the pair (A,C) is not entangled with B, and also the pair (B,C) is not entangled with A. States such as in this example have no multipartite entanglement, they only require bipartite entanglement between two fixed (groups of) systems. However, for certain states called fully inseparable states, entanglement is present for all such groupings—they are multipartite entangled, yet they might still be obtainable from statistical mixtures of states with only bipartite entanglement, and all states of this type are called biseparable. Only quantum systems that cannot be thought of as being created from bipartite entanglement alone are called genuine multipartite entanglement (GME) and such states have therefore previously been considered to be of special significance.

In a somewhat surprising turn of events, recent studies have found that this separation into biseparable and GME states only holds when a single instance (or “copy”) of the quantum systems is considered. In technical terms, it has been shown that all fully inseparable biseparable (FIB) states of finite-dimensional quantum systems become GME when multiple copies are considered jointly. This phenomenon, which does not require carrying out any operations on these quantum states, was dubbed multi-copy activation of GME.

In this paper we show that this phenomenon does not only occur in finite-dimensional quantum systems, like, for instance, the polarization of some fixed number of photons, but in all quantum systems, including infinite-dimensional continuous-variable (CV) systems, such as, e.g., those used to describe the electromagnetic field in laser beams. In our investigation we further find that a GME test that has previously been believed to identify certain (Gaussian) CV states as belonging to the set of FIB states does not allow such a conclusion: We show that some states that were thought to be FIB based on this test are actually GME.

► BibTeX data

@article{Baksova2025multicopyactivation,
  doi = {10.22331/q-2025-04-09-1699},
  url = {https://doi.org/10.22331/q-2025-04-09-1699},
  title = {Multi-copy activation of genuine multipartite entanglement in continuous-variable systems},
  author = {Baksov{\'{a}}, Kl{\'{a}}ra and Leskovjanov{\'{a}}, Olga and Mi{\v{s}}ta Jr., Ladislav and Agudelo, Elizabeth and Friis, Nicolai},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1699},
  month = apr,
  year = {2025}
}

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Cited by

[1] Nicky Kai Hong Li, Xi Dai, Manuel H. Muñoz-Arias, Kevin Reuer, Marcus Huber, and Nicolai Friis, "Detecting genuine multipartite entanglement in multi-qubit devices with restricted measurements", Nature Communications 17 1, 1707 (2026).

[2] Robert Stárek, Tim Gollerthan, Olga Leskovjanová, Michael Meth, Peter Tirler, Nicolai Friis, Martin Ringbauer, and Ladislav Mišta, "Experimental Verification of Multicopy Activation of Genuine Multipartite Entanglement", Physical Review Letters 136 16, 160201 (2026).

[3] Swati Choudhary, Ujjwal Sen, and Saronath Halder, "Protocols for sharing genuine multipartite entanglement by employing copies of biseparable states", Physical Review A 114 1, 012463 (2026).

[4] E. Shchukin and P. van Loock, "Revisiting Gaussian genuine entanglement witnesses with modern software", Physical Review Research 8 2, 023124 (2026).

[5] Lisa T. Weinbrenner, Klára Baksová, Sophia Denker, Simon Morelli, Xiao-Dong Yu, Nicolai Friis, and Otfried Gühne, "Superactivation and Incompressibility of Genuine Multipartite Entanglement", arXiv:2412.18331, (2024).

[6] E. Shchukin and P. van Loock, "Revisiting Gaussian genuine entanglement witnesses with modern software", arXiv:2412.09757, (2024).

[7] Olga Leskovjanová, Klára Baksová, Jan Provazník, Ladislav Mišta, and Nicolai Friis, "On the existence of fully inseparable biseparable Gaussian states", arXiv:2605.28404, (2026).

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