We find an algebraic formula for the N-partite concurrence of N qubits in an X matrix. X matrices are density matrices whose only nonzero elements are diagonal or antidiagonal 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 in which each qubit interacts with a local amplitude damping channel. It is shown that only one type of GHZ state loses its entanglement in finite time; for the rest, N-partite entanglement dies out asymptotically. Algebraic formulas for the entanglement dynamics are given in both cases. We directly confirm that the half-life of the entanglement is proportional to the inverse of N. When entanglement vanishes in finite time, the time at which entanglement vanishes can decrease or increase with N depending on the initial state. In the macroscopic limit, this time is independent of the initial entanglement.
|Original language||English (US)|
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|State||Published - Dec 5 2012|
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics