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arXiv:1209.4197 · New Journal of Physics

Tomographic characterization of correlations in a photonic tripartite state

Andrea Chiuri, L Mazzola, Mauro Paternostro, Paolo Mataloni

Published Aug 1, 2012• 8 citations
arXivHTMLPDF

Abstract

Starting from a four-partite photonic hyper-entangled Dicke resource, we report the full tomographic characterization of three-, two- and one-qubit states obtained by projecting out part of the computational register. The reduced states thus obtained correspond to fidelities with the expected states larger than 87%, therefore certifying the faithfulness of the entanglement-sharing structure within the original four-qubit resource. The high quality of the reduced three-qubit state allows for the experimental verification of the Koashi–Winter relation for the monogamy of correlations within a tripartite state. We show that, by exploiting the symmetries of the three-qubit state obtained upon projection over the four-qubit Dicke resource, such a relation can be experimentally fully characterized using only five measurement settings. We highlight the limitations of such an approach and sketch an experimentally oriented way of overcoming them.

DOI
10.1088/1367-2630/14/8/085006

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Starting from a four-partite photonic hyper-entangled Dicke resource, we report the full tomographic characterization of three-, two- and one-qubit states obtained by projecting out part of the computational register. The reduced states thus obtained correspond to fidelities with the expected states larger than 87%, therefore certifying the faithfulness of the entanglement-sharing structure within the original four-qubit resource. The high quality of the reduced three-qubit state allows for the experimental verification of the Koashi–Winter relation for the monogamy of correlations within a tripartite state. We show that, by exploiting the symmetries of the three-qubit state obtained upon projection over the four-qubit Dicke resource, such a relation can be experimentally fully characterized using only five measurement settings. We highlight the limitations of such an approach and sketch an experimentally oriented way of overcoming them.
We present the experimental observation of the symmetric four-photon entangled Dicke state with two excitations |D_{4};{(2)}. A simple experimental setup allowed quantum state tomography yielding a fidelity as high as 0.844+/-0.008. We study the entanglement persistency of the state using novel witness operators and focus on the demonstration of a remarkable property: depending on the orientation of a measurement on one photon, the remaining three photons are projected into both inequivalent classes of genuine tripartite entanglement, the Greenberger-Horne-Zeilinger and W class. Furthermore, we discuss possible applications of |D_{4};{(2)} in quantum communication.
Entanglement is the crucial resource in the field of quantum information processing and consequently a better understanding of its properties is very desirable. While for bipartite entangled qubit states many tools for characterization exist and also the experimental implementation of the tools is feasible, the situation for multipartite entangled states is different: The available tools have to be suited for a much greater diversity of entanglement properties, e.g. to analyze all the different entanglement classes [1]. A full experimental characterization via state tomography is increasingly difficult as the number of necessary measurement settings grows exponentially with the number of particles. In this contribution we focus on efficient, non-tomographic methods to characterize experimentally observed, multipartite entangled states. First steps towards this goal were demonstrated recently, for instance, for the proof of genuine multipartite entanglement [2] or for the analysis of the persistency of entanglement under loss [3]. Such methods can be further optimized by tailoring them to particular properties of states. We show how three important characteristic quantities, the fidelity, the non-separability and the permutation symmetry, can be evaluated with a significantly lower number of measurement settings than required for a complete tomography. Although the determination of these particular properties provides less information than the reconstruction of the complete density matrix, it allows to judge how well state characteristics are reproduced experimentally. This might be important with respect to an experimental application of states in quantum information. Exemplarily we apply the analysis tools to two genuinely four-qubit entangled states: the Dicke state with two excitations |D 4 〉 [4] and the cluster state |C4 〉 [5, 6]. These states are relevant for particular tasks: The state |D 4 〉 is a resource for telecloning [7], cluster states find an application in one-way quantum computation [6, 8] and are a subgroup of graph states, which play an important role for quantum error correction.
We report the experimental demonstration of two quantum networking protocols, namely quantum 1→3 telecloning and open-destination teleportation, implemented using a four-qubit register whose state is encoded in a high-quality two-photon hyperentangled Dicke state. The state resource is characterized using criteria based on multipartite entanglement witnesses. We explore the characteristic entanglement-sharing structure of a Dicke state by implementing high-fidelity projections of the four-qubit resource onto lower-dimensional states. Our work demonstrates for the first time the usefulness of Dicke states for quantum information processing.
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.
An experimental scheme, its hardware implementation, and procedure for experimental verification of tripartite quantum state sharing and perfect teleportation of the two-qubit photonic state using four different multipartite quantum channels is presented. The four multipartite channels considered are (1) a pair of Greenberger–Horne–Zeilinger triplets, (2) a six-particle cluster state, (3) a highly entangled five-particle Brown state, and (4) a highly entangled six-particle Borras state. In this experiment, optical pulses are delivered by a high repetition rate mode-locked pulsed laser and arbitrary photonic states, in the two-qubit Bloch sphere, are created by the spontaneous parametric down-conversion of optical pulses in a nonlinear crystal. The experimental implementation of the scheme is based on both single-particle and two-particle complete Bell-state measurements, and the unitary transformation required for reconstruction of the qubit is performed using single- and two-qubit operations. Two-qubit operations are implemented using the quantum controlled phase and C-NOT gates. Relative comparison among different multipartite channels along with experimental difficulties and their solutions are also discussed.
We present an experimental and theoretical characterization of the sym- metric four-qubit entangled Dicke state with two excitations D (2) . We investigate the state's violation of local realism and study its characteristic properties with re- spect to quantum information applications. For the experimental observation of the state we used photons obtained from parametric down conversion. This allowed, in a simple experimental set-up, quantum state tomography yielding a fidelity as high as 0.844 ± 0.008.