Multipartite Entanglement Detection via Structure Factors

Krammer, Philipp; Kampermann, Hermann; Bruß, Dagmar; Bertlmann, Reinhold A.; Kwek, L. C.; Macchiavello, Chiara

doi:10.1103/physrevlett.103.100502

Cited by 76 publications

(90 citation statements)

References 37 publications

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“…The entanglement-sharing structure of the state has been characterized quantitatively using a structural entanglement witness for symmetric Dicke states [22,23] and fidelity-based entanglement witnesses for the three-and two-qubit states achieved upon subjecting the Dicke register to proper single-qubit projections [13]. All such criteria have confirmed the theoretical expectations with a high degree of significance.…”

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confidence: 58%

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Experimental Quantum Networking Protocols via Four-Qubit Hyperentangled Dicke States

et al. 2012

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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. PACS numbers: 42.50.Dv,03.67.Bg,42.50.Ex Networking offers the benefits of connectivity and sharing, often allowing for tasks that individuals are unable to accomplish on their own. This is known for computing, where grids of processors outperform the computational power of single machines or allow the storage of much larger databases. It should thus be expected that similar advantages are transferred to the realm of quantum information. Quantum networking, where a given task is pursued by a lattice of local nodes sharing (possibly entangled) quantum channels, is emerging as a realistic scenario for the implementation of quantum protocols requiring medium/large registers. Key examples of such approach are given by quantum repeaters [1], non-local gates [2], scheme for light-mediated interactions of distant matter qubits [3] and one-way quantum computation [4].In this scenario, photonics is playing an important role: the high reconfigurability of photonic setups and outstanding technical improvements have facilitated the birth of a new generation of experiments (performed both in bulk optics and, recently, in integrated photonic circuits [5]) that have demonstrated multi-photon quantum control towards high-fidelity computing with registers of a size inaccessible until only recently [6][7][8][9][10][11]. The design of complex interferometers and the exploitation of multiple degrees of freedom of a single photonic information carrier have enabled the production of interesting states, such as cluster/graph states, GHZ-like states and (phased) Dicke states [12][13][14], among others [15,16]. Dicke states have been successfully used to characterize multipartite entanglement close to fully symmetric states and its robustness to decoherence [14]. They are potentially useful resource for the implementation of protocols for distributed quantum communication such as quantum secret sharing [17], quantum telecloning (QTC) [18], and open destination teleportation (ODT) [19,20]. So far, such opportunities have only been examined theoretically and confirmed indirectly [12,13], leaving a full implementation of such protocols unaddressed.In this Letter, we report the experimental demonstration of 1→ 3 QTC and ODT of logical states using a four-qubit symmetric Dicke state with two excitations realized using a highquality hyperentangled (HE) photonic resource [14,21]. The entanglement-sharing ...

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supporting

confidence: 58%

“…First, we have ascertained the genuine multipartite entangled nature of the state at hand by using tools designed to assess the properties of symmetric Dicke states [22,23,28]. We have considered the multipartite entanglement witness…”

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confidence: 99%

Experimental Quantum Networking Protocols via Four-Qubit Hyperentangled Dicke States

et al. 2012

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“…Several entanglement criteria relying solely on two-body expectation values have been proposed [54]. In particular, in [55] the possibility of addressing two-body statistics (although not individually) via collective observables was exploited.…”

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confidence: 99%

Nonlocality in many-body quantum systems detected with two-body correlators

et al. 2015

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Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, "theorist-and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two-and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Science 344, 1256[Science 344, (2014. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states-ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.

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“…This constitutes a generalization of the witnesses introduced in Krammer et al [57], Cramer et al [58], De Chiara and Sanpera [59], Hauke et al [60]. Going beyond Hauke et al [60], we analyze here the "optimal" witness, obtained by minimizing W f over all f .…”

Section: Optimal Local Entanglement Witnessmentioning

confidence: 99%

Probing entanglement in adiabatic quantum optimization with trapped ions

et al. 2015

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Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol. From exact numerical simulations for small systems and linear ramps, however, we find no substantial correlations with the entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms.

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Multipartite Entanglement Detection via Structure Factors

Cited by 76 publications

References 37 publications

Experimental Quantum Networking Protocols via Four-Qubit Hyperentangled Dicke States

Experimental Quantum Networking Protocols via Four-Qubit Hyperentangled Dicke States

Nonlocality in many-body quantum systems detected with two-body correlators

Probing entanglement in adiabatic quantum optimization with trapped ions

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