Maximally entangled mixed states of two qubits - art. no. 012316

We consider mixed states of two qubits and show under which global unitary operations their entanglement is maximized. This leads to a class of states that is a generalization of the Bell states. Three measures of entanglemen t are considered: entanglement of formation, negativity, and relative entro py of entanglement. Surprisingly all states that maximize one measure also maximize the; others. We give a complete characterization of these generali zed Bell states and prove that these states for fixed eigenvalues are all e quivalent under local unitary transformations. Furthermore we characterize all nearly entangled states closest to the maximally mixed state and derive a lower bound on the volume of separable mixed states.