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We study the connection between the Hilbert-Schmidt measure of entanglement(that is the minimal distance of an entangled state to the set of separablestates) and entanglement witness in terms of a generalized Bell inequalitywhich distinguishes between entangled and separable states. A method forchecking the nearest separable state to a given entangled one is presented. Weillustrate the general results by considering isotropic states, in particular2-qubit and 2-qutrit states -- and their generalizations to arbitrarydimensions -- where we calculate the optimal entanglement witnesses explicitly.Comment: 16 pages, 5 figure

Optimal entanglement witnesses for qubits and qutrits