  We find an algebraic formula for the N-partite concurrence of N qubits in an
X-matrix. X- matricies are density matrices whose only non-zero elements are
diagonal or anti-diagonal when written in an orthonormal basis. We use our
formula to study the dynamics of the N-partite entanglement of N remote qubits
in generalized N-party Greenberger-Horne-Zeilinger (GHZ) states. We study the
case when each qubit interacts with a partner harmonic oscillator. It is shown
that only one type of GHZ state is prone to entanglement sudden death; for the
rest, N-partite entanglement dies out momentarily. Algebraic formulas for the
entanglement dynamics are given in both cases.
