Genuinely Multipartite Concurrence of N-qubit X Matrices (Author's Final Manuscript)
ROCHESTER UNIV NY ROCHESTER United States
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We find an algebraic formula for the N-partite concurrence of N qubits in an X-matrix. X-matrices 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 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.
- Quantum Theory and Relativity