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arXiv:quant-ph/0409036 · Physical Review Letters

Multipartite Entanglement Detection in Bosons

Carolina Alves, Dieter Jaksch

Published Sep 7, 2004• 103 citations
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Abstract

We propose a simple quantum network to detect multipartite entangled states of bosons and show how to implement this network for neutral atoms stored in an optical lattice. We investigate the special properties of cluster states, multipartite entangled states, and superpositions of distinct macroscopic quantum states that can be identified by the network.

DOI
10.1103/physrevlett.93.110501

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We propose a simple quantum network to detect multipartite entangled states of bosons and show how to implement this network for neutral atoms stored in an optical lattice. We investigate the special properties of cluster states, multipartite entangled states, and superpositions of distinct macroscopic quantum states that can be identified by the network.
We investigate the detection and characterization of entanglement based on the quantum network introduced in Phys. Rev. Lett. 93, 110501 (2004) for different experimental scenarios. We first give a detailed discussion of the ideal scheme where no errors are present and full spatial resolution is available. Then we analyze the implementation of the network in an optical lattice. We find that even without any spatial resolution entanglement can be detected and characterized in various kinds of states including cluster states and macroscopic superposition states. We also study the effects of detection errors and imperfect dynamics on the detection network. For our scheme to be practical these errors have to be on the order of one over the number of investigated lattice sites. Finally, we consider the case of limited spatial resolution and conclude that significant improvement in entanglement detection and characterization compared to having no spatial resolution is only possible if single lattice sites can be resolved.
The future of quantum communication relies on quantum networks composed by observers sharing multipartite quantum states. The certification of multipartite entanglement will be crucial to the usefulness of these networks. In many real situations it is natural to assume that some observers are more trusted than others in the sense that they have more knowledge of their measurement apparatuses. Here we propose a general method to certify all kinds of multipartite entanglement in this asymmetric scenario and experimentally demonstrate it in an optical experiment. Our results, which can be seen as a definition of genuine multipartite quantum steering, give a method to detect entanglement in a scenario in between the standard entanglement and fully device-independent scenarios, and provide a basis for semi-device-independent cryptographic applications in quantum networks.
An optical lattice with cold trapped atoms represents a quantum system of fundamental importance as it enables the study of quantum many-body system in a controllable way. It is thus necessary to develop theoretical and experimental tools to explore quantum correlation in such systems to advance our understanding of many-body physics. While previous works have identified some profound aspects of quantum entanglement using e.g. entanglement entropy, there exists a critical demand to have an experimentally accessible tool to investigate many-body quantum entanglement in a broad context. We present an entanglement criterion characterizing collective entanglement in Boson lattice systems and enabling experimental observation readily. On applying our approach to the extended Bose-Hubbard model, we show that our criterion witnesses phase transitions such as Mott insulator--superfluid and Mott insulator--charge density wave transitions. Remarkably, it also makes it possible to detect multipartite entanglement among boson lattice sites in a rigorous sense. Our criterion can be experimentally tested via Raman scattering or time-of-flight methods, which are within the reach of current technology.
Entanglement is a fundamental resource for quantum information processing [1-3], its applications including scalable quantum communication, secure quantum key distribution protocols for cryptography, and exponential speedup of quantum algorithms. It occurs naturally in manybody systems at low temperatures: This makes cold atoms good candidates to provide entangled states involving a large number of particles. For realizing and manipulating such states, an essential task is quantifying the actual amount of entanglement contained in the created state before using it for quantum information protocols. However, this task represents a major challenge, as it requires either full state tomography, scaling exponentially in the system size, or the assumption of unverified system characteristics such as its Hamiltonian or temperature. In this experiment [4], we obtain a quantification of multipartite entanglement from readily accessible measurements - that is, time-of-flight atomic density distribution - based on a recent proposal [5]. We directly observe and quantify the multipartite spatial entanglement between the sites of a periodic optical potential (optical lattice) that hosts massive bosonic particles. We characterize its behaviour when crossing the superfluid-Mott insulator transition and when varying temperature, demonstrating the robustness of our method. References [1] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (Cambridge, 2000). [2]R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865-942 (2009). [3]O. Göhne and G. Tóth, Entanglement detection, Physics Reports 474, 1-75 (2009). [4]M. Cramer, A. Bernard, N. Fabbri, L. Fallani, C. Fort, S. Rosi, F. Caruso, M. Inguscio, and M. B. Plenio, Entanglement of bosons in optical lattices, E-print arXiv:1302.4897 [5]M. Cramer, M. B. Plenio, and H. Wunderlich, Measuring entanglement in condensed matter systems, Phys. Rev. Lett. 106, 020401 (2011).
The topology of classical networks is determined by physical links between nodes, and after a network request the links are used to establish the desired connections. Quantum networks offer the possibility to generate different kinds of entanglement prior to network requests, which can substitute links and allow one to fulfill multiple network requests with the same resource state. We utilize this to design entanglement-based quantum networks tailored to their desired functionality, independent of the underlying physical structure. The kind of entanglement to be stored is chosen to fulfill all desired network requests (i.e. parallel bipartite or multipartite communications between specific nodes chosen from some finite set), but in such a way that the storage requirement is minimized. This can be accomplished by using multipartite entangled states shared between network nodes that can be transformed by local operations to different target states. We introduce a clustering algorithm to identify connected clusters in the network for a given desired functionality, i.e. the required network topology of the entanglement-based network, and a merging algorithm that constructs multipartite entangled resource states with reduced memory requirement to fulfill all desired network requests. This leads to a significant reduction in required time and resources, and provides a powerful tool to design quantum networks that is unique to entanglement-based networks.