Genuinely Multipartite Concurrence of N-qubit X-matrices

TL;DR

This paper derives an algebraic formula for the N-partite concurrence of N-qubit X-matrices and applies it to analyze entanglement dynamics in GHZ states under local interactions, revealing conditions for entanglement sudden death.

Contribution

It provides the first explicit algebraic formula for N-partite concurrence of N-qubit X-matrices and applies it to study entanglement dynamics in GHZ states.

Findings

Only one GHZ state type is prone to entanglement sudden death.

N-partite entanglement generally dies out momentarily for most states.

Algebraic formulas describe entanglement dynamics under local harmonic oscillator interactions.

Abstract

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.