Lower bound on entanglement of formation for the qubit-qudit system

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has derived a closed formula for the entanglement of formation (EOF) of an arbitrary mixed state in a system of two qubits. There is no known closed-form expression for the EOF of an arbitrary mixed state in any system more complicated than two qubits. This paper, via a relatively straightforward generalization of Wootters’ original derivation, obtains a closed-form lower bound on the EOF of an arbitary mixed state of a system composed of a qubit and a qudit (a d-level quantum system, with d>~3). The derivation of the lower bound is detailed for a system composed of a qubit and a qutrit (d=3); the generalization to d>3 then follows readily.