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

Abstract: Meyer and Wallach proposed the average norm squared of the wedge products of the projections of a state onto the single qubit subspaces as the global entanglement measure. Meyer and Wallach's global entanglement has the significant impact. We propose the average determinant of reduced density matrices for each qubit as a global entanglement measure. We show that these two measures are the same algebraically though they use different concepts. By means of the properties of reduced density matrices, we can explore 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, the average mixedness for each qubit and 1-tangle almost vanish for large number of qubits. We also point out that for two quits, the present measure is just the square of the concurrence while for three qubits, the present measure is or greater than 3-tangle.