Optimal entanglement enhancement for mixed states

We consider the actions of protocols involving local quantum operations and classical communication (LQCC) on a single system consisting of two separated qubits. We give a complete description of the orbits of the space of states under LQCC and characterize the representatives with maximal entanglement of formation. We thus obtain a LQCC entanglement concentration protocol for a single given state (pure or mixed) of two qubits which is optimal in the sense that the protocol produces, with nonzero probability, a state of maximal possible entanglement of formation. This defines a new entanglement measure, the maximum extractable entanglement.