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Optimal Entanglement Witnesses for Qubits and Qutrits

Reinhold A. Bertlmann·Katharina Durstberger·Beatrix C. Hiesmayr·Philipp Krammer
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Abstract

We study the connection between the Hilbert-Schmidt measure of entanglement (that is the minimal distance of an entangled state to the set of separable states) and entanglement witness in terms of a generalized Bell inequality which distinguishes between entangled and separable states. A method for checking the nearest separable state to a given entangled one is presented. We illustrate the general results by considering isotropic states, in particular 2-qubit and 2-qutrit states -- and their generalizations to arbitrary dimensions -- where we calculate the optimal entanglement witnesses explicitly.

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Reinhold A. Bertlmann, Katharina Durstberger, Beatrix C. Hiesmayr, Philipp Krammer. 2005-08-04. Optimal Entanglement Witnesses for Qubits and Qutrits. https://doi.org/10.1103/physreva.72.052331

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