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arXiv:2008.01599 · Optica

Verifying genuine multipartite entanglement of the whole from its separable parts

Michal Mičuda, Robert Stárek, Jan Provazník, Olga Leskovjanová, Ladislav Mišta

Published Jul 11, 2019• 6 citations
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Abstract

We prove experimentally the predicted existence of a three-qubit quantum state with genuine multipartite entanglement which can be certified solely from its separable two-qubit reduced density matrices. The qubits are encoded into different degrees of freedom of a pair of correlated photons and the state is prepared by letting the photons to propagate through a linear optical circuit. The presence of genuine multipartite entanglement is verified by finding numerically a fully decomposable entanglement witness acting nontrivially only on the reductions of the global state. Our result confirms viability of detection of emerging global properties of composite quantum systems from their parts which lack the properties.

DOI
10.1364/optica.6.000896

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Genuine multipartite entanglement underlies correlation experiments corroborating quantum mechanics and it is an expedient empowering many quantum technologies. One of many counterintuitive facets of genuine multipartite entanglement is its ability to exhibit an emergent character. That is, one can infer its presence in some multipartite states merely from a set of its separable marginals. Here we show that the effect can also be found in the context of Gaussian states of bosonic systems. Specifically, we construct examples of multimode Gaussian states carrying genuine multipartite entanglement which can be verified solely from separable nearest-neighbor two-mode marginals. The key tool of our construction is an entanglement witness acting only on some two-mode reductions of the global covariance matrix, which we find by a numerical solution of a semidefinite program. We also propose an experimental scheme for preparation of the simplest three-mode state, which requires interference of three correlatively displaced squeezed beams on two beam splitters. Besides revealing the concept of emergent genuine multipartite entanglement in the Gaussian scenario and bringing it closer to experimentally testable form, our results pave the way to effective diagnostics methods of global properties of multipartite states without complete tomography.
Genuine multipartite entanglement underlies correlation experiments corroborating quantum mechanics and it is an expedient empowering many quantum technologies. One of many counterintuitive facets of genuine multipartite entanglement is its ability to exhibit an emergent character, that is, one can infer its presence in some multipartite states merely from a set of its separable marginals. Here, we show that the effect can be found also in the context of Gaussian states of bosonic systems. Specifically, we construct examples of multimode Gaussian states carrying genuine multipartite entanglement which can be verified solely from separable nearest-neighbour two-mode marginals. The key tool of our construction is a genuine multipartite entanglement witness acting only on some two-mode reductions of the global covariance matrix, which we find by a numerical solution of a semi-definite programme. We also propose an experimental scheme for preparation of the simplest three-mode state, which requires interference of three correlatively displaced squeezed beams on two beam splitters. Besides revealing the concept of emergent genuine multipartite entanglement in the Gaussian scenario and bringing it closer to experimentally testable form, our results pave the way to effective diagnostics methods of global properties of multipartite states without complete tomography.
We study the genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states with arbitrary dimensions based on correlation tensors. Effective criterion is derived to verify the genuine multipartite entanglement. Detailed examples are given to show that the criterion detects more genuine multipartite entanglement than the existing criteria.
Genuine multipartite entanglement and full inseparability are two inequivalent quantum resources. Even though all genuinely multipartite entangled states are also fully inseparable, not all fully inseparable states are genuinely multipartite entangled. There exist fully inseparable states that can be prepared as convex mixtures of states separable with respect to different bipartite splits. Here, we are interested in examples of Gaussian states that possess this type of entanglement, so-called fully inseparable biseparable states. We show for several archetypical families of multimode Gaussian states that fully inseparable biseparable candidate states are actually genuinely multipartite entangled. Using projections to finite-dimensional subspaces and fully decomposable witnesses, we observe a shrinking of the regions of potentially fully inseparable biseparable Gaussian states with growing dimension of the projection subspaces. We therefore conjecture that all fully inseparable Gaussian states are genuinely multipartite entangled.
Multipartite entanglement is a key resource for quantum technologies, yet its certification typically relies on correlations from measurements involving all particles, making it increasingly vulnerable to imperfections as the system size grows. Here we report the first experimental demonstration of genuine multipartite entanglement detection from correlations with the minimum possible nontrivial support, known as the entanglement detection length (EDL). Using a photonic platform, we certify W, Dicke, and cluster states with entanglement witnesses constructed from correlations at the EDL. In particular, we verify genuine multipartite entanglement of three- and four-qubit W states and a four-qubit Dicke state using two-body correlations, and of a four-qubit cluster state using three-body correlations. For the four-photon Dicke state, we further show that this minimal-correlation strategy is more robust than the compared global witness under the analyzed local-basis-misalignment model. We also find that, within the witness families considered here, increasing the number of measured subsets enhances the tolerance to noise. These results establish entanglement detection at the EDL limit as a measurement-efficient route to multipartite entanglement certification.