A comparison of the entanglement measures negativity and concurrence

Abstract

In this paper we investigate two different entanglement measures in the case of mixed states of two qubits. We prove that the negativity of a state can never exceed its concurrence and is always larger than √[(1 − C)² + C²] − (1 − C), where C is the concurrence of the state. Furthermore, we derive an explicit expression for the states for which the upper or lower bound is satisfied. Finally we show that similar results hold if the relative entropy of entanglement and the entanglement of formation are compared.