Variance Measure of Coherence of Quantum Pure States

We provide an expression for the measure of coherence of quantum pure states, which is obtained by quantifying the deviation or distance between the measured state and the maximally coherent states in the same Hilbert space. We classify quantum pure states in a Hilbert space according to their coherence and prove that the variance measure of coherence is proper for all quantum pure states. We demonstrate that the variance measure of coherence is simpler and easier to obtain than the l1-norm of coherence and the relative entropy of coherence.