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arXiv:0902.4372 · Physical Review A

Detection and typicality of bound entangled states

Joonwoo Bae, Markus Tiersch, Simeon Sauer, Fernando de Melo, Florian Mintert, Beatrix C. Hiesmayr, Andreas Buchleitner

Published Aug 13, 2009• 18 citations
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Abstract

We derive an explicit analytic estimate for the entanglement of a large class of bipartite quantum states, which extends into bound entanglement regions. This is done by using an efficiently computable concurrence lower bound, which is further employed to numerically construct a volume of $3\ifmmode\times\else\texttimes\fi{}3$ bound entangled states.

DOI
10.1103/physreva.80.022317

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We derive an explicit analytic estimate for the entanglement of a large class of bipartite quantum states, which extends into bound entanglement regions. This is done by using an efficiently computable concurrence lower bound, which is further employed to numerically construct a volume of 3\ifmmode×\else\texttimes\fi33\ifmmode\times\else\texttimes\fi{}33\ifmmode×\else\texttimes\fi3 bound entangled states.
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.