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arXiv:1004.1655 · Open Systems & Information Dynamics

A Class of Bell Diagonal States and Entanglement Witnesses

Dariusz Chruściński, Andrzej Kossakowski, Krzysztof Młodawski, Takashi Matsuoka

Published Sep 1, 2010• 13 citations
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Abstract

We analyze special class of bipartite states — so-called Bell diagonal states. In particular, we provide new examples of bound entangled Bell diagonal states and construct the class of entanglement witnesses diagonal in the magic basis.
DOI
10.1142/s1230161210000138

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We show how to detect entangled, bound entangled and separable bipartite quantum states of arbitrary dimension and mixedness using geometric entanglement witnesses. These witnesses are constructed using properties of the Hilbert–Schmidt geometry and can be shifted along parameterized lines. The involved conditions are simplified using Bloch decompositions of operators and states. As an example we determine the three different types of states for a family of two-qutrit states that is part of the 'magic simplex', i.e. the set of Bell-state mixtures of arbitrary dimension.