Detection of genuine N-Qubit W state, GHZ state and Twin-Fock state via Quantum Fisher information

We study the entanglement detection of three classes of state in the white noise model: N-qubit W state, Greenberger-Horne-Zeilinger state and Twin-Fock state. Taking advantage of Quantum Fisher information, we first present how to witness M-separable W state (M <= N) in the ideal situation, and then derive the criteria for detecting genuine W state, Greenberger-Horne-Zeilinger state and Twin-Fock state in the noisy model. Meanwhile, the bounds for M-separable W state, k-partite entangled GHZ state and k-partite entangled Twin-Fock state are also investigated. The results show that with the increase of the number of particles, the requirement of visibility V for genuine multipartite entanglement becomes more and more stringent, while it is relaxed for partial entanglement. Specially, an extremum value of V-WN = 1/3 is found in the limit of large N. (C) 2020 Elsevier B.V. All rights reserved.