Entanglement of formation of an arbitrary state of two qubits

Abstract

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 ρ is the minimum average entanglement of an ensemble of pure states that represents ρ. An earlier paper 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 for special states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing decompositions. © 1998 The American Physical Society.