### Abstract

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) |
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Article number | 062303 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 86 |

Issue number | 6 |

DOIs | |

State | Published - Dec 5 2012 |

Externally published | Yes |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*86*(6), [062303]. https://doi.org/10.1103/PhysRevA.86.062303