Lower bound on entanglement of formation for the qubit-qudit system
E. Gerjuoy · Physical Review A · 2003
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.