Genuinely multipartite concurrence of N -qubit X matrices

By S. Rafsanjani, Marcus Huber, C. Broadbent, Joseph H. Eberly. 2012

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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 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.Westudythecaseinwhicheachqubitinteractswithalocalamplitude 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 .W hen 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3d610161d51201ddf646b7f5b051b07042b8a36d