  The entanglement of a pure state of a pair of quantum systems is defined as
the entropy of either member of the pair. The entanglement of formation of a
mixed state is defined as the minimum average entanglement of an ensemble of
pure states that represents the given mixed state. An earlier paper [Phys. Rev.
Lett. 78, 5022 (1997)] conjectured an explicit formula for the entanglement of
formation of a pair of binary quantum objects (qubits) as a function of their
density matrix, and proved the formula to be true for a special class of mixed
states. The present paper extends the proof to arbitrary states of this system
and shows how to construct entanglement-minimizing pure-state decompositions.
