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arXiv:1603.05802 · Physical Review Letters

Multipartite Entanglement of a Two-Separable State

Stefan Gerke, Jan Sperling, W. Vogel, Yin Cai, Jonathan Roslund, Nicolas Treps, Claude Fabre

Published Sep 9, 2016• 50 citations
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Abstract

We consider a six-partite, continuous-variable quantum state that we have effectively generated by the parametric down-conversion of a femtosecond frequency comb. We show that, though this state is two-separable, i.e., it does not exhibit "genuine entanglement," it is undoubtedly multipartite entangled. The consideration of not only the entanglement of individual mode decompositions, but also of combinations of those, solves the puzzle and exemplifies the importance of studying different categories of multipartite entanglement.

DOI
10.1103/physrevlett.117.110502

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We consider a six-partite, continuous-variable quantum state that we have effectively generated by the parametric down-conversion of a femtosecond frequency comb. We show that, though this state is two-separable, i.e., it does not exhibit "genuine entanglement," it is undoubtedly multipartite entangled. The consideration of not only the entanglement of individual mode decompositions, but also of combinations of those, solves the puzzle and exemplifies the importance of studying different categories of multipartite entanglement.
An analysis is conducted of the multipartite entanglement for Gaussian states generated by the parametric down-conversion of a femtosecond frequency comb. Using a recently introduced method for constructing optimal entanglement criteria, a family of tests is formulated for mode decompositions that extends beyond the traditional bipartition analyses. A numerical optimization over this family is performed to achieve maximal significance of entanglement verification. For experimentally prepared 4-, 6-, and 10-mode states, full entanglement is certified for all of the 14, 202, and 115 974 possible nontrivial partitions, respectively.
An analysis is conducted of the multipartite entanglement for Gaussian states generated by the parametric down-conversion of a femtosecond frequency comb.Using a recently introduced method for constructing optimal entanglement criteria, a family of tests is formulated for mode decompositions that extends beyond the traditional bipartition analyses.A numerical optimization over this family is performed to achieve maximal significance of entanglement verification.For experimentally prepared 4-, 6-, and 10-mode states, full entanglement is certified for all of the 14, 202, and 115 974 possible nontrivial partitions, respectively.
Significant progress has been made with multipartite entanglement of discrete qubits, but continuous variable systems may provide a more scalable path toward entanglement of large ensembles. We demonstrate multipartite entanglement in a microwave frequency comb generated by a Josephson parametric amplifier subject to a bichromatic pump. We find 64 correlated modes in the transmission line using a multifrequency digital signal processing platform. Full inseparability is verified in a subset of seven modes. Our method can be expanded to generate even more entangled modes in the near future.
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 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.