2005•Physical Review AOpen access

Optimal entanglement witnesses for qubits and qutrits

Reinhold A. Bertlmann, Katharina Durstberger, Beatrix C. Hiesmayr, Philipp Krammer

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 two-qubit and two-qutrit states---and their generalizations to arbitrary dimensions---where we calculate the optimal entanglement witnesses explicitly.

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Key concepts: Separable state, Quantum entanglement, Entanglement witness, Qutrit, Peres–Horodecki criterion, Multipartite entanglement, Qubit, Measure (data warehouse)