The average determinant of the reduced density matrices for each qubit as a global entanglement measure

Abstract

In this paper, we propose the average determinant of reduced density matrices for each qubit as a global entanglement measure. By means of the properties of reduced density matrices, we can investigate the present measure. We propose a decomposition law for the present measure, demonstrate that the present measure just measures the average mixedness for each qubit and the average 1-tangle, and indicate that for n-qubit W state and Dicke states, the average mixedness for each qubit and 1-tangle almost vanish for the large number of qubits. We also point out that for two qubits, the present measure is just the square of the concurrence while for three qubits, the present measure is the sum of the 3-tangle and the twice the average 2-tangle.