Lower Bound on Entanglement of Formation for the Qubit-Qudit System

Abstract

Wootters [PRL 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 greater than or equal to 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 greater than 3 then follows readily.

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• Universal state inversion and concurrence in arbitrary dimensions
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