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

Hayata Yamasaki1,2, Simon Morelli1,2, Markus Miethlinger1, Jessica Bavaresco1,2, Nicolai Friis1,2, and Marcus Huber2,1

1Institute for Quantum Optics and Quantum Information — IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
2Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Vienna, Austria

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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 $\textit{genuine multipartite entanglement}$ 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.

A centrally important concept in multipartite entanglement theory is the distinction between biseparability and genuine multipartite entanglement (GME). Here, we show that multiple identically prepared copies of biseparable states, readily available in many quantum communication technologies, can result in GME. Indeed, sometimes more than two copies are needed for this to happen, yet, GME activation may occur for states with no distillable bipartite entanglement. Our results thus shed new light on, and even call into question, basic tenets of entanglement theory, and significantly advance the field of multipartite entanglement characterisation by opening up a new frontier beyond the single-copy paradigm.

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[2] Róbert Trényi, Árpád Lukács, Paweł Horodecki, Ryszard Horodecki, Tamás Vértesi, and Géza Tóth, "Multicopy metrology with many-particle quantum states", arXiv:2203.05538.

[3] Carlos Palazuelos and Julio I. de Vicente, "Genuine multipartite entanglement of quantum states in the multiple-copy scenario", arXiv:2201.08694.

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