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arXiv:1101.2001 · Physical Review A

Measure of genuine multipartite entanglement with computable lower bounds

Zhihao Ma, Zhihua Chen, Jing‐Ling Chen, Christoph Spengler, Andreas Gabriel, Marcus Huber

Published Jun 20, 2011• 300 citations
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Abstract

We introduce an intuitive measure of genuine multipartite entanglement, which is based on the well-known concurrence. We show how lower bounds on this measure can be derived and also meet important characteristics of an entanglement measure. These lower bounds are experimentally implementable in a feasible way enabling quantification of multipartite entanglement in a broad variety of cases.

DOI
10.1103/physreva.83.062325

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The problems of genuine multipartite entanglement detection and classification are challenging. We show that a multipartite quantum state is genuine multipartite entangled if the multipartite concurrence is larger than certain quantities given by the number and the dimension of the subsystems. This result also provides a classification of various genuine multipartite entanglements. We present a lower bound of the multipartite concurrence in terms of bipartite concurrences. While various operational approaches are available for providing lower bounds of bipartite concurrences, our results give an effective operational way to detect and classify genuine multipartite entanglement. As applications, genuine multipartite entanglement of tripartite systems is analyzed in detail.
Experimentally quantifying entanglement and coherence is extremely important in quantum information processing. In a multipartite quantum system, usually the fidelity of the system's state compared to a target state is measured to detect its entanglement. The authors present a fidelity-based method to derive experimentally accessible lower bounds for measures of genuine multipartite entanglement and coherence, allowing quick quantification of system states without quantum state tomography in experiments. The method works generally, for several entanglement measures and coherence measures, and examples of real experimental states are analyzed in detail.
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Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we construct observable bounds to multipartite entanglement for systems of arbitrary size, which are functions of the local and global state purities, and correlation functions. First, we derive experimentally accessible upper and lower limits to both the bipartite entanglement of formation and the squashed entanglement of bipartite systems, by leveraging cornerstone results of quantum information theory: the entropy strong subadditivity inequality and the Koashi-Winter monogamy relation. Then, we convert them into bounds to the entanglement up to degree k for arbitrary states, and to the genuine k-partite entanglement, by employing a recently proposed method. Finally, we analytically and numerically test these results, by bounding the multipartite entanglement of several relevant states and mixtures, including the important classes of GHZ, Dicke, W states, and random pure states.