Optimal local preparation of an arbitrary mixed state of two qubits: Closed expression for the single-copy case

We consider the problem of preparing a single copy of an arbitrary two-qubit mixed state, starting from an entangled pure state and using only local operations assisted with classical communication. We present an analytical expression for the minimal amount of pure-state entanglement required, and describe the corresponding local strategy. We also examine optimal probabilistic generalizations of the previous process.