  In this paper, we propose concurrence classes for an arbitrary multi-qubit
state based on orthogonal complement of a positive operator valued measure, or
POVM in short, on quantum phase. In particular, we construct concurrence for an
arbitrary two-qubit state and concurrence classes for the three- and four-qubit
states. And finally, we construct $W^{m}$ and $GHZ^{m}$ class concurrences for
multi-qubit states. The unique structure of our POVM enables us to distinguish
different concurrence classes for multi-qubit states.
